Homework Help: Calculus (Checking Answer)

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
du= 2xdx
du/2= xdx

(1/2) S sqrt(u) du
(1/2)*((u^(3/2))/(3/2))
(1/2)*(2/3)*(u^(3/2))
(1/3)*(u^(3/2))
= (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
du= -3dx
du/-3=dx
x= -((u - 2)/3)

=(-1/3) S (-((u - 2)/3))*(u^(-1/2))
=(-1/3) S ((-((u^(1/2)/3)-((2u^(-1/2))/3))
=(-1/3)*[((2/9)*(u^(3/2))-((4/3)*(u^(1/2))]
=[(-2/27)*((2 - 3x)^(3/2)) + (4/3)*((2 - 3x)^(1/2))] correct/incorrect?

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