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If f(a+b-x)=f(x), then prove that...

If `f(a+b-x)=f(x),` then prove that `int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int0^oo(dx)/(1+x^2)

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  2. If I1=int0^(pi/2)costhetaf(sintheta+cos^2theta)d(theta) and I2=int0^(...

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  3. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf...

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  4. Let I1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dx and I2=int(-3)^1(2(x+1)^2+1...

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  5. Find the value of int0^(pi/2)sin2xdx

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  6. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

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  7. The value of int0^(pi/2)cos^2xdx

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  8. prove that |sint| is non-differentiable at t=pi.

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  9. Find the value of int0^1x(1-x)dx

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  10. Let Sn=sum(k=0)^n n/(n^2+kn+k^2) and Tn=sum(k=0)^(n-1) n/(n^2+kn+k^2) ...

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  11. The value of the definite integral int(sqrt2-1)^(sqrt(2)+1)(x^4+x^2+2...

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  12. If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, the...

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  13. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dx and K=int(-2)^(-1)(6-6x+x^2) t...

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  14. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

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  15. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

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  16. int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to...

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  17. Ifint(-pi/4)^((3pi)/4)(e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx))=kint(-p...

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  18. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x))dx, and I2=int(...

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  19. If f(y)=e^y ,g(y) = y>0,a n d \ F(t)=int0^t f(t-y)g(y)dy ,then

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  20. Given int0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integral ...

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