Why Is My Calculation of the Antiderivative for sqrt(20-x) Incorrect?

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The discussion focuses on the incorrect calculation of the antiderivative for the function sqrt(20-x) over the interval from 0 to 20. The user initially miscalculated the antiderivative as -(2/3)(sqrt(20-x)^(3/2)), which led to an incorrect evaluation of zero at both limits. The correct antiderivative is -(2/3)(20-x)^(3/2), and the user acknowledges the mistake in evaluation, emphasizing that the area under the curve is not zero. Proper evaluation of the antiderivative at the limits is crucial for accurate results.

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hekoshi
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I can't seem to get this antiderivitive correct: sqrt(20-x) from 0 to 20.

I end up with -(2/3)(sqrt(20-x)^(3/2) which is zero evaluated at either of the two limits.

This is not correct since the area below the curve of the original equation is definitely not 0.
 
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You shouldn't have sqrt in your answer since that's already accounted for in the 3/2 exponent. Also, the antiderivative functionis not zero for x = 0. Check it again.
 
Yes and also it is not zero at both the limits; it should work out now.
 
oops, i meant to write -(2/3)(20-x)^(3/2), but yeah, i didn't evaluate it correctly the first time. It should be:

F(b)-F(a)=-(2/3)(20-20)^(3/2)-(-(2/3)(20-0)^(3/2))

*Facepalm* I blame it on lack of sleep, haha.

thanks.
 

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