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If f(x)=int0^x |t-1| dt, where 0 lt= x l...

If `f(x)=int_0^x |t-1| dt`, where `0 lt= x lt= 2` then (a) range of `f(x)` is `[0,1]` (b) `f(x)` is differentiable at `x=1` (c) `f(x)=cos^(-1)x` has two real roots (d) `f^(prime)(1/2)=1/2`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I(...

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  2. Consider the integral int0^(2pi)(dx)/(5-2cosx) making the substitutio...

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  3. If f(x)=int0^x |t-1| dt, where 0 lt= x lt= 2 then (a) range of f(x) i...

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  4. If int0^1(e^(-x)dx)/(1+e^x)=(log)e(1+e)+k , then find the value of k.

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  5. The value of int0^oo (dx)/(1+x^4) is

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  6. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

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  7. If f(x) is continuous for all real values of x , then sum(r=1)^nin...

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  8. F ind the value of int0^1logx dxdot

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  9. If An=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,Bn=int0^(pi/2)((sinn x)/(sinx)...

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  10. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

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  11. The value of int0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

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  12. Evaluate: int0^(1//sqrt(2))(sin^(-1)x)/((1-x^2)^(3//2))dx

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  13. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

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  14. Evaluate: int1^oo (e^(x+1)+e^(3-x))^(-1)dx

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  15. If f(x)=int(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

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  16. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

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  17. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

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  18. Prove that 4 lt= int1^3 sqrt(3+x^2) dx lt= 4sqrt(3)

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  19. If I1=int0^(pi//2)(cos^2x)/(1+cos^2x)dx , I2=int0^(pi//2)(sin^2x)/(1+s...

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  20. Prove that int0^1sqrt((1+x)(1+x^3))\ dx cannot exceed sqrt((15)/8).

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