Definite Integration Question 180

Question: $ \int _{1}^{3}{(x-1)(x-2)(x-3)dx=} $

[Karnataka CET 2002]

Options:

A) 3

B) 2

C) 1

D) 0

Show Answer

Answer:

Correct Answer: D

Solution:

$ I=\int _{1}^{3}{(x-1)(x-2)(x-3)dx} $ .

$ I=\int _{1}^{3}{(x^{3}-6x^{2}+11x-6)dx=[ \frac{x^{4}}{4}-\frac{6x^{3}}{3}+\frac{11x^{2}}{2}-6x ] _{1}^{3}=0.} $