Calculus (Checking Answer)
posted by Chelsea .
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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