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Let f(x)=int1^xsqrt(2-t^2)dtdot Then th...

Let `f(x)=int_1^xsqrt(2-t^2)dtdot` Then the real roots of the equation `x^2-f^(prime)(x)=0` are (a)`+-1` (b) `+-1/(sqrt(2))` (c)`+-1/2` (d) 0 and 1

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Let T >0 be a fixed real number. Suppose f is continuous function su...

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

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

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

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

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

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

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

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

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  11. Q. int0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

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  12. Prove that int0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2)+.... .+ 1/...

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  13. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

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  14. Evaluate: int0^1(1)/((1+x^2)sqrt(1-x^2))dx

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  15. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

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  16. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

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  17. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= pi^2

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  18. Prove that 1 lt underset(0)overset(2)int((5-x)/(9-x^(2)))dx lt 6/5

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  19. If the difference between the roots of the equation x^2+""a x""+""1...

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  20. If m is the least value (global minimum) and M is the greatest value (...

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