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 \sin^2 x \sin 2x dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\frac{\sin ^{4} x}{2}+C$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Integration Techniques

Missouri State University

Oregon State University

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.

02:25

04:15

Evaluate the indefini…

02:03

Evaluate the integral.…

02:33

00:38

Evaluate the indefinite in…

01:55

00:37

00:39

00:33

03:21

Evaluate the given integra…

this problem is from Chapter seven section to Problem number 17 in the book Calculus Early Transcendental eighth Edition by James Stewart And here we have a indefinite integral of sine squared of X times sine of two x. So first thing we can do is apply a double angle formula to rewrite sign of two X So we have integral sign square eggs and then using our our double angle formula for sign. We have two sin x co sign X, the X so we can pull this to outside the integral and combine these signs to get assigned Cube. And this would be a good time to apply a u substitution. Here we can take you to be cynics so that do you is co sign of X dx. So if we use this use sub are integral becomes two times integral of u cubed, do you? We can evaluate this using the power rule for the integral two times U to the fourth power over four plus c. So here we can back substitute from you back to Synnex using our our u substitution. And this to over four becomes a one half. So we end up with signed to the fourth power of X over to plus C. And there's our answer

View More Answers From This Book

Find Another Textbook

02:19

The length of a rectangle is 3 inches more than its width: If the perimeler…

01:57

B. ABCD is a parallelogram: Tell which kind of parallelogram is identified i…

02:08

Write a quadratic inequality in Standard form that illustrates the given sit…

01:15

PARKING A parking lot is constructed in the shape of a parallelogram What is…

08:39

of the circle__ between the circumference and the radius of & circle is …

02:16

PRAEIee For Exercises 12-15, use the given information. Which lines in the f…

02:42

One side of a polygon measures 10 units and the measure of thecorrespond…

02:02

Pascal had a rectangular piece ofpaper: He cut off a corner of the paper: Th…