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Calculus Question - need help?

+3 votes

Consider the integral 3x(x^2+1). In the following, we will evaluate the integral using two methods.

asked Feb 12, 2013 in CALCULUS by angel12 Scholar

1 Answer

+3 votes

ʃ[3x(x2+1)]dx

Distribute terms using distributive property:  a( b + c) = ab + ac

ʃ[3x3+3x] dx

So the original expression equals  ʃ[3x3+3x] dx

Split into two integrals ʃ3x3 dx + ʃ3x dx

Cavalier's quadrate formula: ʃxa =(xa+1) /(a+1)+C.

ʃ3x3 dx = (3x4)/4+C

ʃ3x dx = (3x2)/2+C

So the original integral is equal to (3/4)x4 + (3/2)x2 +C.

answered Feb 12, 2013 by richardson Scholar

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