Download the App!

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

Evaluate the definite integral.

$ \displaystyle \int^{T/2}_0 \sin (2\pi t/T - \alpha) \, dt $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\frac{T}{\pi} \cos \alpha$

02:46

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

University of Nottingham

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

04:26

Evaluate the integral.

01:20

Evaluate the definite inte…

01:12

08:36

Evaluate the integrals.

01:17

00:29

0:00

say that are you is what's in parentheses. This means that our DT would be capital t over to pie, do you? Which means we now have the integral of as you can see from the substitution we did earlier. The lower case t goes away using the power will we know we can now integrate. Obviously negative night, it becomes positive. This is because we have negative co sign you times the constant as are integral. So we end up with negative negative which, as I said, it's positive. Which gives us t over pi times co sign Hey!

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:08

A government researcher is analyzing the relationship betweenretail sale…

00:39

If a 1-way ANOVA is used and the resulting p-value was 0.0003with a leve…

03:33

Find the exact area of the surface obtained by rotating thegiven cur…

02:50

(18.25) A medical experiment compared zinc supplements with aplacebo for…

01:35

The nurse wants to give 3 g of magnesium sulfate and hasavailable a medi…

02:12

The Genetics and IVF Institute conducted a clinical trial of theYSORT me…

06:39

The two regression equations of the variables x and y are:x=19.13-0.87y<…

05:18

From an Urn that contains five red, five white, and five bluechips, we d…

02:44

Let c be the path given by c(t) =(t^2, t, 3) for t ∈[0,1].Find the avera…

05:40

A ball is dropped from a height of 8 ft. The elasticity of theball is su…