💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Evaluate the integral.

$ \displaystyle \int \sin 2 \theta \sin 6 \theta d \theta $

$$\frac{1}{8} \sin 4 \theta-\frac{1}{16} \sin 8 \theta+C$$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Integration Techniques

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:25

Evaluate the following int…

05:51

02:02

07:22

Evaluate the integral.…

04:29

02:01

Evaluate the integrals.

04:00

01:36

07:21

00:32

Evaluate the integral by m…

This problem is from chapter seven, Section two. Problem number forty two in the book Calculus Early. Transcendental. Lt's a Tradition by James Door. We have an indefinite general sign of Tooth Taylor time Sign of six data. So are integral. Our instagram is of the form sign a sign be in our case we have is to data will be a six data so we can rewrite the Inter Grand using this formula here. And the purpose for doing this is that the right hand side will be easier to integrate because the co signs in the signs on the right hand side are not being multiplied together. So is pull out that one half outside the inner girl. We have co sign of two. They don't minus six data minus co Sign of to theatre plus six data. So separate us from our work on the side. So here we can observe that we have to fade on minus six data. So they're sort here is negative forthe Daito. And if we like, we can replace co signer minus for data with co sign of fourth Ada. Since you may recall, that coastline is even not necessary. But it'LL Simplify I work. We have one has integral co signing for data minus cosign a beta Dana. And here in my help to go ahead and apply a u substitution. If you're unsure about these animals here for this one, you could take you to be four Daito. And for this integral, you can take you to be a data. So evaluating these two minute girls, we should obtain sign Fourth eight over four minus sign eight data over eight, plus our constancy. And this could be simplified a little bit. So let's go ahead and do that sign for theta over eight minus. Sign a beta over sixteen. Plus he and there's our answer.

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Evaluate the following integrals.$$\int \sin ^{2}\left(\theta+\frac{\pi}…

Evaluate the integral.$$\int \sin 3 \theta \cos 2 \theta d \theta$$

$ \displaystyle \int_{\frac{\pi}{6}}^{\frac{\…

Evaluate the integral.$$\int_{0}^{\pi / 6} \sec ^{3} 2 \theta \tan 2 \th…

$$\int \sin ^{2} 5 \theta d \theta$$

Evaluate the integrals.$$\int(\sin 2 \theta) e^{\sin ^{2} \theta} d \the…

Evaluate the integrals.$$\int \frac{\sin \theta d \theta}{\cos ^{2} \the…

$ \displaystyle \int \frac{\sec \theta \tan \…

Evaluate the integral.$$\int \sin ^{3} a \theta d \theta$$

Evaluate the integral by making the given substitution.

$ \displays…