Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter 7.3, Problem 1YT

YOUR TURN 1 Repeat Example 1 to approximate ∫ 1 5 4 x d x .

EXAMPLE 1 Approximation of Area

Consider the region bounded by the y - axis , the x - axis , and the graph of f ( x ) = 4 − x 2 , shown in Figure 4.

  1. Approximate the area of the region using two rectangles. Determine the height of the rectangle by the value of the function at the left endpoint.
  2. Repeat part (a) using the value of the function at the right endpoint to determine the height of the rectangle.
  3. Repeat part (a) using the value of the function at the midpoint to determine the height of the rectangle.
  4. We can improve the accuracy of the previous approximations by increasing the number of rectangles. Repeat part (a) using four rectangles.
  5. Repeat part (a) using eight rectangles.

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5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈
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Chapter 7 Solutions

Calculus For The Life Sciences

Ch. 7.1 - YOUR TURN Find an antiderivative of f(x)=8x7.Ch. 7.1 - Prob. 2YTCh. 7.1 - Prob. 3YTCh. 7.1 - Prob. 4YTCh. 7.1 - Prob. 5YTCh. 7.1 - Prob. 6YTCh. 7.1 - YOUR TURN Find an equation of the curve whose...Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3E
Ch. 7.1 - Explain why the restriction n1 is necessary in the...Ch. 7.1 - Prob. 5ECh. 7.1 - Find the following. 9dyCh. 7.1 - Find the following. (2z+3)dzCh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Find the following. x2(x4+4x+3)dxCh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Find the following. (56t5/2+18t7/2)dtCh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Find the following. 13x2dxCh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Find the following. (3x+4e0.4+eo.1)dxCh. 7.1 - Find the following. (9x3e0.4x)dxCh. 7.1 - Prob. 33ECh. 7.1 - Find the following. 2y1/23y26ydyCh. 7.1 - Prob. 35ECh. 7.1 - Find the following. (v2e3v)dvCh. 7.1 - Prob. 37ECh. 7.1 - Find the following. (2y1)2dyCh. 7.1 - Find the following. x+1x3dxCh. 7.1 - Find the following. 12z3z3dzCh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Find the following. (3cosx4sinx)dxCh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - The slope of the tangent line to a curve is given...Ch. 7.1 - LIFE SCIENCE APPLICATIONS Biochemical Excretion If...Ch. 7.1 - LIFE SCIENCE APPLICATIONS Flour Beetles A model...Ch. 7.1 - Concentration of a solute According to the Ficks...Ch. 7.1 - Cell Growth Under certain conditions, the number...Ch. 7.1 - Blood Pressure The rate of change of the volume...Ch. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Motion under gravityShow that an object thrown...Ch. 7.1 - Rocket A small rocket was launched straight up...Ch. 7.1 - Rocket science In the 1999 movie October Sky,...Ch. 7.2 - YOUR TURN Find 8x(4x2+8)6dx.Ch. 7.2 - YOUR TURN Find x33x4+10dx.Ch. 7.2 - YOUR TURN Find x+1(4x2+8x)3dx.Ch. 7.2 - YOUR TURN Find x+3x2+6xdx.Ch. 7.2 - YOUR TURN Find x3ex4dx.Ch. 7.2 - Prob. 6YTCh. 7.2 - Prob. 7YTCh. 7.2 - Prob. 8YTCh. 7.2 - Integration by substitution is related to what...Ch. 7.2 - The following integrals may be solved using...Ch. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 25ECh. 7.2 - Use substitution to find the indefinite integral....Ch. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 30ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 48ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Use substitution to find each indefinite integral....Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Stan and Ollie work on the integral 2x(x2+2)dx....Ch. 7.2 - Outpatient Visits According to the data from the...Ch. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - Prob. 65ECh. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.3 - YOUR TURN 1 Repeat Example 1 to approximate...Ch. 7.3 - Prob. 2YTCh. 7.3 - Explain the difference between an indefinite...Ch. 7.3 - Complete the following statement. 04(x2+3)dx=limn,...Ch. 7.3 - Let f(x)=2x+5, x1=0, x2=2, x3=4, x4=6, and x=2. a....Ch. 7.3 - Let f(x)=1/x, x1=1/2, x2=1, x3=3/2, x4=2, and...Ch. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - In Exercise 5-14, approximate the area under the...Ch. 7.3 - Prob. 11ECh. 7.3 - In Exercise 5-14, approximate the area under the...Ch. 7.3 - In Exercise 5-14, approximate the area under the...Ch. 7.3 - Prob. 14ECh. 7.3 - Consider the region below f(x)=x/2, above the...Ch. 7.3 - Consider the region below f(x)=5x, above the...Ch. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - In Exercises 2631, estimate the area under each...Ch. 7.3 - APPLY IT Foot-and-Mouth Epidemic In 2001, the...Ch. 7.3 - In Exercises 2631, estimate the area under each...Ch. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - DistanceWhen data are given in tabular form, you...Ch. 7.3 - Heat Gain The following graphs show the typical...Ch. 7.3 - Heat Gain The following graphs show the typical...Ch. 7.3 - Automobile VelocityTwo cars start from rest at a...Ch. 7.3 - Distance Musk the friendly pit bull has escaped...Ch. 7.3 - Distance The speed of a particle in a test...Ch. 7.3 - Running In 1987, Canadian Ben Johnson set a world...Ch. 7.3 - Traffic The following graph shows the number of...Ch. 7.4 - YOUR TURN Find 133x2dx.Ch. 7.4 - Prob. 2YTCh. 7.4 - Prob. 3YTCh. 7.4 - Prob. 4YTCh. 7.4 - Prob. 5YTCh. 7.4 - YOUR TURN Find the area under the curve...Ch. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Evaluate each definite integral. 12(5t3)dtCh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Evaluate each definite integral. 23(x23x+5)dxCh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Evaluate each definite integral. 143(2p+1)2dpCh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Evaluate each definite integral. 10y(2y23)5dyCh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Evaluate each definite integral. 0/4sinxdxCh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Evaluate each definite integral. /22/3cosxdxCh. 7.4 - Prob. 36ECh. 7.4 - In Exercises 37-48, use the definite integral to...Ch. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - In Exercises 37-48, use the definite integral to...Ch. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - In Exercises 37-48, use the definite integral to...Ch. 7.4 - 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Prob. 22ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 24ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - LIFE SCIENCE APPLICATIONS Pollution Pollution...Ch. 7.5 - OTHER APPLICATIONS Distribution of Income Suppose...Ch. 7.5 - OTHER APPLICATIONS Net SavingsSuppose a company...Ch. 7.5 - Prob. 36ECh. 7.5 - ProfitCanham Enterprises had an expenditure rate...Ch. 7.5 - Net SavingsA factory of Hollis Sherman Industries...Ch. 7.CR - CONCEPT CHECK Determine whether each of the...Ch. 7.CR - Prob. 2CRCh. 7.CR - Prob. 3CRCh. 7.CR - Prob. 4CRCh. 7.CR - CONCEPT CHECK Determine whether each of the...Ch. 7.CR - Prob. 6CRCh. 7.CR - Prob. 7CRCh. 7.CR - Prob. 8CRCh. 7.CR - Prob. 9CRCh. 7.CR - Prob. 10CRCh. 7.CR - Prob. 11CRCh. 7.CR - Prob. 12CRCh. 7.CR - Prob. 13CRCh. 7.CR - Prob. 14CRCh. 7.CR - 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