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Prove that 4le int(1)^(3) sqrt(3+x^(3)) ...

Prove that `4le int_(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30`.

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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. Evaluate : int(0)^(pi//2)sin^(9)x cos^(7)xdx

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  2. Evaluate : int(0)^(pi//2)cos^(9)xdx

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  3. Prove that 4le int(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30.

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  4. Let I(1)=int(0)^(pi//4)e^(x^(2))dx, I(2) = int(0)^(pi//4) e^(x)dx, I(3...

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  5. The value of the definite integral int0^1(x\ dx)/ (x^3+16) lies in the...

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  6. The maximum and minimum values of the integral. int0^(pi//2)dx/(1+sin^...

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  7. Let f(a)>0, and let f(x) be a non-decreasing continuous function in [a...

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  8. The mean value of the function f(x)= 2/(e^x+1) in the interval [0,2] i...

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  9. Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) ...

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  10. The value of lim(x to oo)(d)/(dx)int(sqrt(3))^(sqrt(x))(r^(3))/((r+1)...

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  11. If a, b and c are real numbers, then the value of underset(trarr0)(lim...

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  12. Let y = f(x) be a differentiable curve satisfying int(2)^(x)f(t)dt=(x...

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  13. If F(x)=(1)/(x^(2))overset(x)underset(4)int [4t^(2)-2F'(t)]dt then F'(...

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  14. Given f(x) where ={(x|x|,"for" xle -1),([x+1]+[1-x],"for"-1lt x lt...

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  15. If I=underset (0)overset(1) int cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx ...

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  16. The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...

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  17. Evaluate int-1^1 [x[1+sinpix]+1]dx, [.] is the greatest integer funct...

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  18. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

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  19. Let overset(a)underset(0)int f(x)dx=lambda and overset(a)underset(0)in...

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  20. The value of the integral overset(pi)underset(0)int (sin k x)/(sin x)...

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