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

Evaluate `int_(1)^(a)x.a^(-[log_(a)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 PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
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  9. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf(x)...

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  10. The value of the integral int3^6 sqrtx/(sqrt(9-x)+sqrtx)dx is

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  11. Find the value of int(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx.

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  12. Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot

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  13. Find the value of int0^1x(1-x)^ndx

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  14. If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, the...

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  15. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

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

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  17. The value of int-pi^pi cos^2x/[1+a^x]dx, a > 0 is

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  18. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

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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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