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

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

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07:43

J Hardin

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Integration Techniques

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.

Frank V.

Is it standard to use Sine Squared to solve this?

Sam L.

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

Alexis B.

What is a inaugural ?

Holly S.

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

Jessica G.

Is it standard to use Pythagorean solve this?

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

0:00

Find the area of the regio…

07:06

05:12

18:19

02:20

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.

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