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If f(x)=int(-1)^(x)|t|dt, then for any x...

If `f(x)=int_(-1)^(x)|t|dt`, then for any `xge0,f(x)` equals

A

`1/2(1-x^(2))`

B

`1/2x^(2)`

C

`1/2(1+x^(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={(int_(-1)^(x)-tdt,-1lexlt0),(int_(-1)^(0)-tdt+int_(0)^(x)tdt, xge0):}={(1/2(1-x^(2)),-1lexlt0),(1/2(1+x^(2)),xge0):}`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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  15. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

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