Answered: Use integration by parts to evaluate…

Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9 and lower limit of -1.7

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.2: Integration By Parts

Problem 41E

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Question

Use integration by parts to evaluate the definite integral:
∫3se^-4s ds with an upper limit of -0.9 and lower limit of -1.7

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1:

$A = 3 \int_{a}^{b} s e^{- 4 s} d s, s o l v i n g A w h e r e a, b a r e u p p e r a n d l o w e r l i m i t s a s p e r q u e s t i o n I n t e g r a t e b y p a r t s w i t h u = s, d v = e^{- 4 s} d s d u = d x, v = \frac{e^{- 4 s}}{- 4} T h u s, A = 3 [{[s \cdot \frac{e^{- 4 s}}{- 4}]}_{a}^{b} - \int_{a}^{b} \frac{e^{- 4 s}}{- 4} d s] = 3 [{[s \cdot \frac{e^{- 4 s}}{- 4}]}_{a}^{b} - {[\frac{e^{- 4 s}}{16}]}_{a}^{b}] n o w p u t t i n g v l a u e s o f a = - 0.9 a n d b = - 1.7 = 3 [{[s \cdot \frac{e^{- 4 s}}{- 4}]}_{- 1.7}^{- 0.9} - {[\frac{e^{- 4 s}}{16}]}_{- 1.7}^{- 0.9}] = - 958.567$

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