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If `f(x)` is differentiable and `int_0^(t^2) x f(x) dx=2/5t^5,` then `f(4/(25))` equals (a)`2/5` (b) `-5/2` (c)`1` (d) `5/2`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. The value of int0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

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

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

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

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

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

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

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

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

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  11. Let T >0 be a fixed real number. Suppose f is continuous function su...

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  12. Evaluate: int0^1 1/(sqrt(1-x^2))sin^(-1)(2xsqrt(1-x^2))dxdot

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  13. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation x...

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  14. Evaluate: int(-pi//2)^(pi//2) sqrt(cosx-cos^3x) dx

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  15. If f(2-x)=f(2+x) and f(4-x)=f(4+x) for all x and f(x) is a function fo...

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  16. int(-1)^2|x^3-x|dxdot

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  17. If f(x) is integrable over [1,2], then int1^2f(x)dx is equal to (a) (...

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  18. Evaluate: int(-pi/2)^(2pi)sin^(-1)(sinx)dx

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  19. The value of int0^(pi/4)sin2xdx is

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  20. Let: an=int0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim(n->o...

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