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

Show that `int_0^pixf(sinx)dx=pi/2int_0^pif(sinx)dxdot`

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Show that, int_(0)^(pi)xf(sinx)dx=(pi)/(2)int_(0)^(pi)f(sinx)dx .

Prove that, int_(0)^(pi)f(sinx)dx=2int_(0)^((pi)/(2))f(sinx)dx .

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

int_0^1(tan^(-1)x)/x dx is equals to (a) int_0^(pi/2)(sinx)/x dx (b) int_0^(pi/2)x/(sinx)dx (c) 1/2int_0^(pi/2)(sinx)/x dx (d) 1/2int_0^(pi/2)(""x)/(sinx)dx

If int_(0)^(pi) x f(sinx) dx=A int_(0)^((pi)/(2))f(sinx)dx , then the value of A is -

int_(0)^(pi)sqrt(1+sinx)dx

Show : int_(0)^((pi)/(2))sinxf(sin2x)dx=int_(0)^((pi)/(2))cosxf(sin2x)dx

By applying the result int_(0)^((pi)/(2))f(cosx)dx=int_(0)^((pi)/(2))f(sinx)dx , evaluate int_(0)^((pi)/(2))sin^(2)xdxandint_(0)^((pi)/(2))cos^(2)xdx .

int_pi^(16pi) abs(sinx) dx=

Evaluate: int_0^pi(dx)/(1+sinx)

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...

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  2. STATEMENT 1: int0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int0^picosx dx...

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  3. STATEMENT 1: Let m be any integer. Then the value of Im=int0^pi(sin2m ...

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  4. STATEMENT 1: inta^xf(t)dt is an even function if f(x) is an odd functi...

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  5. STATEMENT 1: The value of int0^(2pi)cos^(99)x dx is 0 STATEMENT 2: in...

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  6. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  7. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

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  8. Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...

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

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  10. Let f(x) be a non-constant twice differentiable function defined on (-...

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  11. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

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  12. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

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  13. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

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  14. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

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  15. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

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  16. The option(s) with the values of a and L that satisfy the following eq...

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  17. Let f: R->R be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

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  18. Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dx. Hence ...

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  19. Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,...

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  20. If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f(x)]^(-1)dx=sqrt(2), then

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