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First make a substitution and then use integratio…

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Problem 36 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int_0^t e^s \sin (t - s) ds $

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Chapter 7

Techniques of Integration

Section 1

Integration by Parts

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Video Transcript

The problem is, while this is nt grow into your own from zero to t into us arms Sign He minus us? Yes, but this problem we can use my third with integration by parts The farm owner is into girl from a to B. You have absolutely prime yaks If you come too you be from a to B minus integral to being you Prom time slee P X Now for our problem, we can light U s bicultural you two as WeII Prom You speak all to sign in minus then you prom? Yes, they will tow us and re It's Nico too. Call sign minus eyes. Now, by this formula, this integral is you call Teo into us times. Call sign E minus eyes from zero to t minus into go to Ise Time's sign in minus eyes. He us from zero to This is unconscionable that a first term complying He and there are two as they have inter team times will sign. My honesty's a cost zero So this one this is into team minus it was eerie is one on consigned to ministerial offices minus consigned then Linus. But this interior we can also use integration by pars on like you is equal to toe eyes. Big crime. It's legal to sign minus. Then you from asleep too. It wa ce if you can't negative sign in minor size then this integral is the cultural your eyes terms make tio sign. I mean minus us. This is from et tu from there on to I mean and minus auntie go from zero to t you two eyes times make tio fine minus Yes, this's the cartoon into T minus. Consign Andi Minus. This's one with planning tn zero to this term. So we have you know minus it is there are two connective sign. Jesus is past fine. And then mark Plus and to go from zero to Teo two eyes sign minus us. Yes. So this is the count. You you minus call Sign. He minus. Find him Los integral from their own tea. And this is minus ham. Sign the minus us. Yes. Now look at the Sinti girl on this. You know we can find a seam so we can move this term to left hand side than we have should have certainty. Girl, there are tio your eyes. Sign the minus eyes. Yes, this is going to t minus. Sign minus sign. So the thirties, You too. T minus Kasai Human. A scientific over too.

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Problem

First make a substitution and then use integratio…

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Calculus: Early Transcendentals

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Watch More Solved Questions in Chapter 7

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Kayleah Tsai

Caleb Elmore

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Kayleah Tsai

Caleb Elmore

James StewartCalculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Kayleah Tsai

Caleb Elmore

James Stewart

Calculus: Early Transcendentals