Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to $ x $ and $ y $. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.
$ y = \sin x $ , $ y = x $ , $ x = \frac{\pi}{2} $ , $ x = \pi $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Sky Li
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 1
Areas Between Curves
Michael M.
May 13, 2021
these are not the right questions that match the book
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Lectures
06:16
Sketch the region enclosed…
02:32
05:13
05:14
01:25
02:53
09:51
06:31
02:31
Okay, so we need to draw those given curves. First, let's draw x y axis and then draw the first curve which is 6 okay. So, let's draw sine x, we start from negative pi. This goes to 0 and stop at pi. Then we draw i equals to x, which is something like this: it's like the tangent curve of sine x at the region and x equals to pi over 2 here x equals to pi over 2. This is 1. Sin x equals to 1 point. So here there will be 1 and this is x, equals to pi. Okay, so for the bounded region will be this shaded region right here, so our job is evaluate this area. So how do we do it? We find the approximating, since everything we can see here is represented by x. So when we do the integral we do it with respect to x, okay area, where equals to the integral, with respect to x, all right. So if i so good and we need to find the boundary the boundary for x is just goes from pi over 2 pi, and this here is just upper curve minus the lower curve. Before that we can see, we can draw a typical approximating rectangle, something like this. It'S very small here, if they do me do out, it will look like this is approximating rectangle of the will be delta, x and height will be x. I minus sine x. I okay, so in other words our integral will be x, minus sine x. Okay, then they milorade this integral to find the area of the region. The anti derivative of this is the learned, half x square and sine x. Anti derivative of this is negative cosine. I be plus cosine x, i i plus cosine x. Then we evaluate at x equals pi minus x equal to pi over 2, so the first term there will be pi square over 2 and second, a cosine, pi yo, know cosine. We know cosiniative 1. So this is minus 1 minus x equals to pi over 2, so this will be pi squared over 4 times 1 half is pi square over 8 and cosine pi over 2 is 0, so this plus 0 p, in other words our area. There will be pi square over 2 minus pi square over 8, which is 3 pi square over 8 minus 1 point: okay,
View More Answers From This Book
Find Another Textbook
00:33
Write coefficient of x^2 in x^4 +7x^3 + 9x^2 + 11
03:40
Expand a. (x + 2y + 4z)^2 b. (2x – y + z )^2
01:09
Simplify : 101.13 – [36.7 + {13.5 ÷ (3 x 0.5)}] write in copy
01:41
find the square root of 3969 by the division method ?
01:03
Plot the points A(4, 3) and B(-1, 2) on the cartesian plane.
01:46
1. Estimate the quotient: (i) 1010 ÷ 25 (ii) 4295 ÷ 7 (v) 4423 ÷ 21 (vi) 928…
01:27
1. Rao bought notebooks at the rate of 4 for ₹35 and sold them at the rate o…
01:22
1. The local bus service has 2 lines of buses that start together at 8 am. B…
01:04
Three friends start a business and decide to split the profits equally. Susa…
00:55
write true or false root 4 + root 5 equals to root 9