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Evaluate int(1)^(5)sqrt(x-2)sqrt(x-1)dx....

Evaluate `int_(1)^(5)sqrt(x-2)sqrt(x-1)dx`.

Text Solution

Verified by Experts

The correct Answer is:
`2`
`int_(1)^(5)sqrt(x-2sqrt(x-1))dx=int_(1)^(5)sqrt((sqrt(x-1)-1)^(2))dx`
`=int_(1)^(5)|sqrt(x-1)-1|dx`
`=int_(1)^(2)(1-sqrt(x-1))dx+int_(2)^(5)(sqrt(x-1)-1)dx`
`=|x-(2x(x-1)^(3//2))/3|_(1)^(2)+|(2(x-1)^(3//2))/3-x|_(2)^(5)`
`=(2-2/3-1+0)+(16/3-5-2/3+2)=2`
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