Answered: Use integration by parts to evaluate…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter58: Achievement Review—section Five

Section: Chapter Questions

Problem 30AR: Determine dimension x to 3 decimal places.

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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

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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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