Evaluate the integral: {eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^3(\theta) \cos^2(\theta) \, \mathrm{d} \theta {/eq}.
Question:
Evaluate the integral: {eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^3(\theta) \cos^2(\theta) \, \mathrm{d} \theta {/eq}.
U-Substitution:
Replacing some functions from the original integral with a temporary substitute is one of the methods of solving definite or indefinite integrals.
This method is called the u-substitution. It is also called as the integration by substitution.
Answer and Explanation: 1
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View this answerU-substitution must be utilized to determine the value of the given definite integral.
Let
{eq}u = \cos x {/eq}
Then
{eq}\mathrm{d}u = -\sin x...
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Learn more about this topic:
from
Chapter 13 / Lesson 5Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.