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Question

Question: \[\int_{1}^{3}{(x - 1)(x - 2)(x - 3)dx =}\]...

∫13(x−1)(x−2)(x−3)dx=\int_{1}^{3}{(x - 1)(x - 2)(x - 3)dx =}

A

3

B

2

C

1

D

0

Answer

0

Explanation

Solution

I=∫13(x−1)(x−2)(x−3)dxI = \int_{1}^{3}{(x - 1)(x - 2)(x - 3)dx}.

I=∫13(x3−6x2+11x−6)dx=[x44−6x33+11x22−6x]13=0.I = \int_{1}^{3}{(x^{3} - 6x^{2} + 11x - 6)dx = \left\lbrack \frac{x^{4}}{4} - \frac{6x^{3}}{3} + \frac{11x^{2}}{2} - 6x \right\rbrack_{1}^{3} = 0.}