Posted by Chelsea on Tuesday, April 5, 2011 at 5:07pm.
Find the antiderivative by hand in each case.
S stands for the integral sign
A) S x*sqrt(10 + x^2) dx
So, u= 10 + x^2
(1/2) S sqrt(u) du
= (1/3)*(10 + x^2)^(3/2) correct/incorrect?
B) S (x/(sqrt(2 - 3x)))dx
S (x)*(2 - 3x)^(-1/2)
u= 2 - 3x
x= -((u - 2)/3)
=(-1/3) S (-((u - 2)/3))*(u^(-1/2))
=(-1/3) S ((-((u^(1/2)/3)-((2u^(-1/2))/3))
=[(-2/27)*((2 - 3x)^(3/2)) + (4/3)*((2 - 3x)^(1/2))] correct/incorrect?
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