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- If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...
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- STATEMENT 1: int0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int0^picosx dx...
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- STATEMENT 1: Let m be any integer. Then the value of Im=int0^pi(sin2m ...
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- STATEMENT 1: inta^xf(t)dt is an even function if f(x) is an odd functi...
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- STATEMENT 1: The value of int0^(2pi)cos^(99)x dx is 0 STATEMENT 2: in...
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- For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...
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- Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...
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- Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...
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- Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot
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- Let f(x) be a non-constant twice differentiable function defined on (-...
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- 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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- Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...
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- Let f: R rarr R be a continuous odd function, which vanishes exactly a...
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- If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...
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- Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...
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- The option(s) with the values of a and L that satisfy the following eq...
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- Let f: R->R be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...
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- Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dx. Hence ...
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- Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,...
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- If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f(x)]^(-1)dx=sqrt(2), then
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