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Find the area bounded by the curve y=(x-...

Find the area bounded by the curve `y=(x-1)(x-2)(x-3)` lying between the ordinates `x=0a n dx=3.`

A

`(9)/(4)`

B

`(11)/(4)`

C

`(11)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(0)^(3)|(x-1)(x-2)(x-3)|dx=int_(0)^(3)|x^(3)-6x^(2)+11x-6|dx`

`A=-int_(0)^(1)(x^(3)-6x^(2)+11x-6)dx+int_(1)^(2)(x^(3)-6x^(2)+11x-6)dx-int_(2)^(3)(x^(3)-6x^(2)+11x-6)dx`
`A=(11)/(4)`
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