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Evaluate int(1)^(a)x.a^(-[log(e)x])dx,(a...

Evaluate `int_(1)^(a)x.a^(-[log_(e)x])dx,(agt1)`.Here `[.]` represents the greatest integer function.

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Verified by Experts

The correct Answer is:
`1/2(a^(2)-1)`
`Iltxlta`
or `0ltlog_(a)xlt1`
or `[log_(a)x]=0`
`:.I=int_(1)^(a)x dx=1/2 (a^(2)-1)`
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CENGAGE ENGLISH-DEFINITE INTEGRATION -CAE_TYPE
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  13. Find the value of int0^1x(1-x)^ndx

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  16. Find the value of int(0)^(pi//2)sin2xlogtanxdx.

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  18. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  19. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  20. Find the value of int(0)^(2pi)1/(1+tan^(4)x)dx

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