Calculus - Standalone book
Calculus - Standalone book
3rd Edition
ISBN: 9781464125263
Author: Jon Rogawski, Colin Adams
Publisher: W.H. Freeman & Co
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Chapter 8, Problem 1CRE
To determine

To match the integrals (a)-(e) with their anti-derivatives (i)-(v) on the basis of the general form (do no evaluate the integrals).

Expert Solution & Answer
Check Mark

Answer to Problem 1CRE

Solution:

We have hence determined that (a) matches (v), (b) matches (iv), (c) matches (iii), (d) matches (i) and (e) matches (ii)

Explanation of Solution

Compare the integrals and the functions without evaluating the integrals to identify the correct match

Given:

(a) xdxx24 (b) (2x+9)dxx2+4 (c) sin3xcos2xdx (d) dxx16x21

(e) 16dxx(x4)2

(i) sec14x+C (ii) log|x|log|x4|4x4+C

(iii) 130(3cos5x3cos3xsinx27cos3x)+C

(iv) 92tan1x2+ln(x2+4)+C (v) x24+C

Calculation:

(a) xdxx24 - since x is a constant multiple of the derivative x24, the substitution method implies that the integral is a constant multiple of duu,u=x24 that is a constant multiple of u. This hence matches the function in (v)

(b) (2x+9)dxx2+4 - 2xdxx2+4corresponds to ln(x2+4) and hence matches (iv)

(c) sin3xcos2xdx - the reduction formula shows that this integral is the sum of constant multiples of products and hence matches the function in (iii)

(d) dxx16x21- since dx|x|x21=sec1x+Cwhich corresponds to the function in (i)

(e) 16dxx(x4)2- This one matches the function in (ii)

Conclusion:

We have hence determined that (a) matches (v), (b) matches (iv), (c) matches (iii), (d) matches (i) and (e) matches (ii).

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Chapter 8 Solutions

Calculus - Standalone book

Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - 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