Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Evaluate the integral.

$ \displaystyle \int x \sin^2 x \cos x\ dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$$\frac{1}{3} x \sin ^{3} x+\frac{1}{3} \cos x-\frac{1}{9} \cos ^{3} x+C$$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Missouri State University

University of Nottingham

Idaho State University

Boston College

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.

02:49

00:51

Evaluate the indefinite in…

01:47

Evaluate the integral.…

03:08

Let's try this one by using parts. Let's take you to be this X over here. Do you use the X? And then we're left over with this for our D V. And then here you can do a U sub that you be signed. And he's the power rule. So here, using the formula, the by parts formula there we have U times V. So that's X. Thank you. Be over three and then minus integral. And then we have Z do pull over three and then here. Let's go ahead and rewrite this as science square time sign and then use the Pythagorean identity. And then yeah, right that So we have actually, let's go to the next page here and then split this up into two winner girls double negative turns into a plus. And then here you could do another use of and after evaluating this, Okay, so here we have a plus co sign over three and then here a minus co sign cubed. And then here we'll have to divide by another three from the power rule. Sell 10 9. Wow! And that's our final answer.

View More Answers From This Book

Find Another Textbook

01:55

Question 8 01A bus covers a distance of 375 km at a certainspeed in …