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Find the antiderivative $ F $ of $ f $ that satisfies the given condition. Check your answer by comparing the graphs of $ f $ and $ F $.

$ f(x) = 5x^4 - 2x^5 $, $ \quad F(0) = 4 $

$c=4$

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Missouri State University

Oregon State University

Harvey Mudd College

Boston College

we're being told to find the antidrug F that satisfies two given condition. And then we are to check an answer by comparing the grass of effort. And so, um, we are going Teo, first of all, find the time to go of SFX. So to protect the integral of effort backs a reminder that this will give us and Capitol effort. That's was Dan to do it with a custom constancy. So let's go ahead and begin integrating. So this is going to be fly X to the Ford minus two. Acted in Fear D eg and this is a relatively It's very simple. Auntie do everyday way just simply usedto act. But also there's going to be five x to the fifth over. If I minus two acts to the sixth off six plus C and then that's going to simplify to X to the fifth minus X to the sixth over three. It's going to be a plus C, and this is affects and F zero is equal to four. So if you plug ins you ugo minus Theo over three plus C, they go there for all these are cancel. House is going to see is equal to four, and that is our answer