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Problem 51 Hard Difficulty

Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take $ C = 0 $).

$ \displaystyle \int e^{\cos x} \sin x \, dx $

Answer

$-e^{\cos x}+C$

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Video Transcript

Okay. We know we have the integral of feed to the coastline. Axe, sign axe detox. Which means that if you is co sign axe, then d'you is negative. Sign acts D ox, which means now we have negative times the integral of each of the U do you, which is equivalent to negative. You know, the year plus c remember, we come back. Substitute US coast on X, giving us negative e to the coastline ax plus c now to Graff, the integral Aiken graph first. Now the function As you know, we have minimum. When the off on FX, the function changes from negative to positive maximum when it changes from positive to negative. This proves we have a reasonable answer.