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JH

Evaluate the integral.$\displaystyle \int_0^{\frac{\pi}{4}} \tan^3 \theta \sec^2 \theta\ d \theta$

$\frac{1}{4}$

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Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

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Video Transcript

Let's do a U substitution here, take you to be tan of data, then do you equal sequence Where? Data. So let's go ahead and rewrite this. So watch out for those limits of integration. Here we have zero. It's a plug that in for data zero. So that's how new are lower Limit similarly for the upper limit plug that in U equals ten pyro for that's one. And then step back here. That's our one. And then we have Are you cubed right here? And this remaining term here in green, That's our deal. Seize the power rule here. You forthe over four zero one plugging that in point and then when you plug in zero, you get zero. So that's a final answer.

JH

Topics

Integration Techniques

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Lectures

Join Bootcamp