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int1^(e^(17//2)) (cos(pi log x))/(x) dx ...

`int_1^(e^(17//2)) (cos(pi log x))/(x) dx =`

A

0

B

minus 1

C

2

D

1

Text Solution

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The correct Answer is:
D
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int0^(pi//2) log(tan x)dx =

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  2. int0^1 (x^4 + 2x^2 + 1)d(x^2 + 1) =

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  3. int1^(e^(17//2)) (cos(pi log x))/(x) dx =

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  4. int0^(2a) (f(x))/(f(x)+f(2a-x)) dx =

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  5. The value of int(-1/2)^(1/2) (cosx). log ((1-x)/(1+x)) dx is

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  6. int0^(pi/8) tan^(2) (2x) dx =

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  7. If int0^x f(t) dt = x + intx^l tf (t) dt, then the value of f(1) is :

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  8. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  9. lim(n rarr oo) 1/n sum(r=1)^(2n) r/squeroot(n^(2)+r^(2)) equals

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  10. The value of the integral int0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n...

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  11. Let f(x) = x - [x], for every real number x, where [x] is integral par...

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  12. int(pi//4)^(3pi//4) (dx)/(1 + cos x) is equal to :

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  13. Let f(x) = int1^x sqrt(2 - t^2)dt. Then the real roots of the equation...

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  14. The integral int(-1/2)^(1/2) {[x]+log((1+x)/(1-x))} dx equals

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  15. The value of (5050 int0^(1) (1-x^(50))^(100)dx)/(int0^(1) (1-x^(50))^(...

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  16. lim(x rarr pi/4)( int2^(sec^(2)x) f(t) dt)/(x^(2)-pi^(2)/16) equals

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  17. The values of lim(x rarr 0) (1)/(x^(3)) int(0)^(x) (t In (1 + t))/(t^(...

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  18. lim(n rarr oo) {(1^(m)+2^(m)+3^(m)+…….+n^(m))/(n^(m+1))} equals

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  19. If I(1) = int0^(1) 2^(x^(2)) dx, I(2) = int0^(1) 2^(x^(3)) dx, I(3) = ...

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  20. The value of the integral, int3^6 (sqrt(x))/(sqrt(9 - x) + sqrt(x))dx ...

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