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Evaluate the integral by making the given substitution.$\int \cos ^{3} \theta \sin \theta d \theta, \quad u=\cos \theta$

$-\frac{\cos ^{4} \theta}{4}+C$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Oregon State University

Harvey Mudd College

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.

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this question tells us to evaluate the integral by making the given substitution. As you can see, they've told us to make the substitution that you was co sign of data. Therefore, negative D'You is signed. Data defeat a duck's remember the derivative of coastline is negative sign which gives us negative you to the fourth because we're increasing exploded by one dividing by the new exponents And now we're back substituting in instead of you It should be negative. Co signed the fourth of data divide by four plus C.

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