Problem

Find the area of the region bounded by the given …

04:44

Problem 57 Hard Difficulty

Find the area of the region bounded by the given curves.

$ y = \sin^2 x $ , $ y = \sin^3 x $ , $ 0 \le x \le \pi $

Answer

$$
\frac{1}{2} \pi-\frac{4}{3}
$$

Discussion

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Jessica G.

September 22, 2020

Is it standard to use Pythagorean solve this?

Holly S.

September 22, 2020

Yes Jessica, Basically it is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

Alexis B.

September 22, 2020

What is a inaugural ?

Sam L.

September 22, 2020

Hey Alexis, I think it is a marking the beginning of an institution, activity, or period of office.

Frank V.

September 22, 2020

Is it standard to use Sine Squared to solve this?

Hank S.

September 22, 2020

Yes Frank, basically it is defined as the composite of the square function and the sine function. Hope that helps.

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Video Transcript

for this given exercise we want to find the area bounded by the curve. So we have sine squared X. Mhm. Okay. Yeah and then we also have cubed And we're focusing on the interval from 0 to Pi. So looking here where X equals pi, this is the area between the curve that we're focused on. So it would be best if we had this value right here, the sign X squared minus the sine cubed dx. So we'll have the integral From 0 to Pi of sin X squared minus Synnex cube Jax. And we'll put parentheses around this whole thing. So once we evaluate this we get about 2.237 which is the same thing as one half pi minus four thirds. So that's our final answer.

Carson M.

California Baptist University

Topics

Integration Techniques

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Problem