Calculus & Its Applications (14th Edition)
Calculus & Its Applications (14th Edition)
14th Edition
ISBN: 9780134437774
Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar
Publisher: PEARSON
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Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
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Chapter 9.6, Problem 22E
To determine

The value of the improper integral ∫1∞2x3/2dx whenever it is convergent.

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Determine whether each integral is convergent or divergent. to (ii) 4 dx dr (x+6) A
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". [.. 1.8 -1.9x dx
2) Determine whether the integral converges or diverges. Justify your answer in each case using proper integral and limit notation. If the integral converges, find its exact value. 10 dx 3√x

Chapter 9 Solutions

Calculus & Its Applications (14th Edition)

Ch. 9.1 - (Review) Differentiate the following functions:...Ch. 9.1 - Use the substitution u=3x to determine e3/xx2dx.Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...
Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Determine the integrals in Exercises 136 by making...Ch. 9.1 - Figure 1 shows graphs of several functions f(x)...Ch. 9.1 - Figure 2 shows graphs of several functions f(x)...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals using indicated...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals using the...Ch. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Determine the following integrals by making an...Ch. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Determine 2x(x2+5)dx by making a substitution....Ch. 9.2 - Evaluate the following integral. xe3xdxCh. 9.2 - Evaluate the following integral. lnxdxCh. 9.2 - Evaluate the following integral. xe5xdxCh. 9.2 - Evaluate the following integral. xex2dxCh. 9.2 - Evaluate the following integral. x(x+7)4dxCh. 9.2 - Evaluate the following integral. x(2x+3)...Ch. 9.2 - Evaluate the following integral. xexdxCh. 9.2 - Evaluate the following integral. x2exdxCh. 9.2 - Evaluate the following integral. xx+1dxCh. 9.2 - Evaluate the following integral. x3+2xdxCh. 9.2 - Evaluate the following integral. e2x(13x)dxCh. 9.2 - Evaluate the following integral. (1+x)2e2xdxCh. 9.2 - Evaluate the following integral. 6xe3xdxCh. 9.2 - Evaluate the following integral. x+2e2xdxCh. 9.2 - Evaluate the following integral. xx+1dxCh. 9.2 - Evaluate the following integral. x2xdxCh. 9.2 - Evaluate the following integral. xlnxdxCh. 9.2 - Evaluate the following integral. x5lnxdxCh. 9.2 - Evaluate the following integral. xcosxdxCh. 9.2 - Evaluate the following integral. xsin8xdxCh. 9.2 - Evaluate the following integral. xln5xdxCh. 9.2 - Evaluate the following integral. x3lnxdxCh. 9.2 - Evaluate the following integral. lnx4dxCh. 9.2 - Evaluate the following integral. ln(lnx)xdxCh. 9.2 - Evaluate the following integral. x2exdxCh. 9.2 - Evaluate the following integral. lnx+1dxCh. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Evaluate the following integral using techniques...Ch. 9.2 - Figure 1 shows graphs of several functions f(x)...Ch. 9.2 - Figure 2 shows graphs of several functions f(x)...Ch. 9.2 - Evaluate xex(x+1)2dx using integration by parts....Ch. 9.2 - Evaluate x7ex4dx. [Hint: First, make a...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 4ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 8ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Prob. 13ECh. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals:...Ch. 9.3 - Evaluate the following definite integrals: 1elnxdxCh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Exercises 24 and 25, find the area of the...Ch. 9.3 - Prob. 25ECh. 9.4 - Consider 13.4(5x9)2dx. Divide the interval 1x3.4...Ch. 9.4 - Prob. 2CYUCh. 9.4 - Prob. 3CYUCh. 9.4 - Prob. 4CYUCh. 9.4 - Prob. 5CYUCh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Refer to the graph in Fig. 11. Apply the...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Approximate the following integrals by the...Ch. 9.4 - Approximate the following integrals by the...Ch. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - The following integrals cannot be evaluated in...Ch. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Area To determine the amount of water flowing down...Ch. 9.4 - Distance Traveled Upon takeoff, the velocity...Ch. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Consider 12f(x)dx, where f(x)=3lnx. Make a rough...Ch. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Technology Exercises In Exercises 3740,...Ch. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.5 - The integral formula is used in many applications...Ch. 9.5 - Present value Find the present value of a...Ch. 9.5 - Present valueA continuous stream of income is...Ch. 9.5 - Present valueFind the present value of a...Ch. 9.5 - Prob. 4ECh. 9.5 - Present value Find the present value of a...Ch. 9.5 - Present valueA continuous stream of income is...Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.6 - Prob. 1CYUCh. 9.6 - Prob. 2CYUCh. 9.6 - Prob. 3CYUCh. 9.6 - In Exercises 1-12, determine if the given...Ch. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - In Exercises 1-12, determine if the given...Ch. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Find the area under the graph of y=1x2forx2.Ch. 9.6 - Prob. 14ECh. 9.6 - Find the area under the graph of y=ex/2forx0.Ch. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 22ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 24ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 30ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 32ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Evaluate the following improper integrals whenever...Ch. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43ECh. 9.6 - Prob. 44ECh. 9.6 - Prob. 45ECh. 9.6 - Prob. 46ECh. 9.6 - Prob. 47ECh. 9.6 - Prob. 48ECh. 9.6 - Prob. 49ECh. 9.6 - Prob. 50ECh. 9 - Describe integration by substitution in your own...Ch. 9 - Prob. 2CCECh. 9 - Prob. 3CCECh. 9 - Prob. 4CCECh. 9 - Prob. 5CCECh. 9 - Prob. 6CCECh. 9 - Prob. 7CCECh. 9 - Prob. 8CCECh. 9 - Prob. 9CCECh. 9 - Prob. 10CCECh. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Determine the following indefinite integral:...Ch. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Determine the following indefinite integral:...Ch. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Evaluate the following definite integrals:...Ch. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Evaluate the following improper integrals whenever...Ch. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RE
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