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Consider the function f(x) satisfying th...

Consider the function `f(x)` satisfying the relation `f(x+1)+f(x+7)=0AAx in Rdot` STATEMENT 1 : The possible least value of `t` for which `int_a^(a+t)f(x)dx` is independent of `ai s12.` STATEMENT 2 : `f(x)` is a periodic function.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int(-pi//4)^(pi//4)log(sinx+cosx)dx

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  2. If alpha,beta(beta>alpha), are the roots of g(x)=a x^2+b x+c=0 and f...

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  3. Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx ...

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  4. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

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  5. Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2), then find th...

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  6. Prove that inta^bf(x)dx=int(a+c)^(b+c)f(x-c)dx , and when f(x) is odd ...

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  7. Evaluate: int0^(100pi)sqrt((1-cos2x))dxdot

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  8. Evaluate: int0^pi(x dx)/(1+cosalphasinx),w h e r e0ltalphaltpidot

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  9. Evaluate : int0^(pi/4)(sinxcosx)/(sin^4x+cos^4x)\ dx

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  10. A periodic function with period 1 is integrable over any finite interv...

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  11. Evaluate: intcos^3xe^(logsinx)dx

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  12. The value of the integral int(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(e^(x-pi...

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  13. Ifint0^(npi)f(cos^2x)dx=kint0^pif(cos^2x)dx ,t h e nfin dt h ev a l u ...

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  14. int(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha ...

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  15. Evaluate: int0^a(dx)/(x+sqrt((a^2-x^2)))orint0^(pi/2)(d theta)/(1+tant...

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  16. Suppose that F(x) is an anti derivative of f(x)=(sinx)/x, where xgt0. ...

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  17. Evaluate: int(-pi)^pi(xsinx dx)/(e^x+1)

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  18. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,then lambda is e...

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  19. Show that int0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

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  20. The number of positive continuous f(x) defined in [0,1] for with I(1)=...

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