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Problem 52 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 \sin x \cos^4 x \, dx $

Answer

$-\frac{\cos ^{5} x}{5}+C$

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Video Transcript

Okay. The first thing we know is that you is co sign axe, which means that negative d'you is equivalent to sign acts. DX won't take the drug, but everyone transfer the negative over to the left hand side. Over here is you could see which means this is equivalent to the integral negative times the integral of you to the fourth d'you using the power ruled. This means we increase the expletive by 125 divided by the expert at five back substitute end co sign. Okay, Now we are at the point where we can grass and it continues on words like that. As you can seek, the answer is reasonable because we can see the graph of f is zero in capital F has a local extreme A. We see its negative when we see it's decreasing in positive months, increasing