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Evaluate 01(x+1)(x2)dx...

Evaluate 01(x+1)(x2)dx

A.

76

B.

56

C.

56

D.

76

Correct answer is D

Expanding (x+1)(x2)=x22x+x2=x2x2

01(x2x2)dx=[x33x222x]01

= [03022×0(1331222×1)]

= 0+13+122=76

Note: This can also be solved using integration by parts. 

uvdx=uvdxu(vdx)dx.