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Problem

Find the area of the region bounded by the given …

04:44

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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 $


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07:43

JH

J Hardin

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
hS

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.

FV

Frank V.

September 22, 2020

Is it standard to use Sine Squared to solve this?

Sl

Sam L.

September 22, 2020

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

AB

Alexis B.

September 22, 2020

What is a inaugural ?

HS

Holly S.

September 22, 2020

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

JG

Jessica G.

September 22, 2020

Is it standard to use Pythagorean solve this?

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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

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Watch More Solved Questions in Chapter 7

Problem 1
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Problem 7
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Problem 9
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Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
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Problem 20
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Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
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Problem 38
Problem 39
Problem 40
Problem 41
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Problem 48
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Problem 50
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Problem 53
Problem 54
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Problem 57
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Problem 59
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Problem 61
Problem 62
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Problem 64
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Problem 66
Problem 67
Problem 68
Problem 69
Problem 70

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.

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Top Calculus 2 / BC Educators
Catherine Ross

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Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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

Join Course
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