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int (-1)^(2) |x|^(3) dx is equal to...

` int _(-1)^(2) |x|^(3) dx` is equal to

A

`5/4`

B

`17/4`

C

`15/4`

D

`4/5`

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(-1)^(2)|x|^(3)dx=int_(-1)^(0)-x^(3)dx+int_(0)^(2)x^(3)dx=-[(x^(4))/(4)]_(-1)^(0)+[(x^(4))/(4)]_(0)^(2)`
`=-(1)/(4)[0-1]+(1)/(4)[2^(4)]=(1)/(4)+4=(17)/(4)`
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