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int0^x[cost]dt ,w h e r ex in (2npi,2npi...

`int_0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot]` denotes the greatest integer function . then the value of` f(1/pi) is`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. If int(0)^(oo) (sinx)/x dx=(pi)/2, then int(0)^(oo) (sin^(3)x)/x dx i...

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  2. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

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  3. int0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot] de...

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  4. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

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  5. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

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  6. f(x) is continuous function for all real values of x and satisfies int...

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  7. Prove that int0^1xe^xdx=1

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  8. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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  9. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

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  10. For x in R and a continuous function f, let I1=int(sin^2t)^(1+cos^2t)...

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  11. Evaluate of each of the following integrals int(pi//6)^(pi//3)(sqrt...

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  12. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  13. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

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  14. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

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  15. Evaluate: int(-pi)^(3pi)log(s e c theta-t a ntheta)d theta

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  16. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

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  17. Let P(x) be a polynomial of least degree whose graph has three points ...

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  18. IfIn=int0^1(dx)/((1+x^2)^n),w h e r en in N , which of the following...

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  19. If f(0)=1,f(2)=3,f^'(2)=5,then find the value of int0^1xf^('')(2x)d...

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  20. Ifinta^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h e n b=22 ,a=2 (b) b=15 ,1=-...

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