Solved: Finding area Find the area of the region enclosed

Chapter 8, Problem 52E

(choose chapter or problem)

Finding area Find the area of the region enclosed by the curve $y = x cos x$ and the $x-axis$ (see the accompanying figure) for

a. $\pi / 2 \leq x \leq 3 \pi / 2$

b. $3 \pi / 2 \leq x \leq 5 \pi / 2$

c. $5 \pi / 2 \leq x \leq 7 \pi / 2$

d. What pattern do you see? What is the area between the curve and the $x-axis$ for

$\left(\frac{2 n-1}{2}\right) \pi \leq x \leq\left(\frac{2 n+1}{2}\right) \pi$,

$n$ an arbitrary positive integer? Give reasons for your answer.

Equation Transcription:

$y=x\ cos\ x$

$x-axis$

$\pi{}/2\leq{}x\leq{}3\pi{}/2$

$3\pi{}/2\ \leq{}x\leq{}5\pi{}/2$

$5\pi{}/2\ \leq{}x\leq{}7\pi{}/2$

$(\frac{2n-1}{2})\pi{}\leq{}x\leq{}\left({\frac{2n+1}{2}\ }\right)\pi{}$

$n$

Text Transcription:

y = x cos x

x-axis

pi/2 leq x leq 3 pi /2

3 pi /2 leq x leq 5 pi /2

5 pi/2 leq x leq 7 pi/2

(2n-1 / 2)pi leq x leq (2n + 1 / 2) pi

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