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If overset(1)underset(0)int(sint)/(1+t)d...

If `overset(1)underset(0)int(sint)/(1+t)dt=alpha`, them the value of the integral `overset(4pi)underset(4pi-2)int("sin"(t)/(2))/(4pi+2-t)dt` in terms of `alpha` is given by

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A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
  1. State whether the statements are true or false.If y=int0^xf(t)dt .Then...

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  2. State whether the statements are true or false.int0^(pi/2)dx/(sqrt(sin...

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  3. If int0^a{f(x)+f(-x)}dx=int-a^aphi(x)dxthen phi(x)=.

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  4. Evaluate: int0^pi (cos x)/(1+sinx)^2 dx

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  5. The value int(-pi/4)^(pi/4)x^2sin^-1xdx=.

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  6. If int0^pi x f(sinx) dx=A int0^(pi/2) f(sinx)dx, then A is (A) pi/2 (B...

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  7. The value of int0^(pi/2)sin2x.log tanxdx is

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  8. If int0^1e^t/(t+1) dt=a, then int(b-1)^b e^(-t)/(t-b-1) dt=

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  9. Evaluateint(-pi/2)^(pi/2)(sin2x)/(1+cos^3x)dx

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  10. If f is a continuous function on the interval [a,b] and there exists ...

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  11. If l(n)=int(1)^(e)(log x)^(n) d x, "then" l(n)+nl(n-1) equal to

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  12. If f(x)=|x-21|+|x-1|then evaluate int-2^2f(x)dx.

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  13. If f(x)=f(4-x), g(x)+g(4-x)=3 and int(0)^(4)f(x)dx=2, then : int(0)^(4...

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  14. It is known that f(x) is an odd function and has a period p. Prove tha...

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  15. The value of int(0)^(2)x^([x^(2)+1])(dx), where [x] is the greatest in...

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  16. Let f(x)=[b^(2)+(a-1)b+2]x-int(sin^(2)x+cos^(4)x)dx be an increasing f...

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  17. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

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  18. If overset(1)underset(0)int(sint)/(1+t)dt=alpha, them the value of the...

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  19. Evaluate: int0^(pi/2) sin^2x/(sinx+cosx)dx

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  20. The point of extremum of f(x)=int0^x(t-2)^2(t-1)dt is a

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