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int0^(2) [2x]dx =, where [.] denotes the...

`int_0^(2) [2x]dx =`, where [.] denotes the greatest function.

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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int sqrtx. e^(sqrtx) dx =

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  2. int0^(10) x^(10)/((10-x)^((10))+x^(10)) dx =

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  3. int0^(2) [2x]dx =, where [.] denotes the greatest function.

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  4. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

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  5. If [.] stands for the greatest integr function, int1^(2)[3x]dx =

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  6. int0^(6) |x-3|dx=

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  7. If f(x) be a continous function for all real values of x and satisfies...

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  8. If f(x) = int(2x)^(sinx) cos (t^(3)) dt then f '(x)

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  9. Iff(x) = int1^(x^(2)) tan^(-1) sqrtt dt, t gt 0, then f^(')(1)=

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  10. If int0^x f(t) dt = x + intx^l tf (t) dt, then the value of f(1) is :

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

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  12. Equation of the tangent to y= int(x^(2))^(x^(3)) (dt)/(sqrt(1+t^(2)))...

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  13. If inta^(x) f(t) dt - int0^(y) g(t) dt = b then dy/dx at (x(0),y(0)) i...

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  14. If f(x) = 1/x^(2) int2^(x)[t^(2)+f^(')(t)]dt, then f^(')(2) =

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  15. If inta^(x) [f(t) - 3t] dt = a^(2)-x^(2) then f(pi/6) =

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  16. Let f(x) = int2^(x) (dt)/(sqrt(1+t^(4)))and g be the inverse of f. The...

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  17. If f and g are continuous [0,a) satisfying f(x) = f(a-x) and g(x)+ g(a...

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  18. Let f : [1, oo) rarr [2, oo) be a differentiable function such that f(...

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  19. The critical point of : f(x) = 1 + x + int1^x [(log t)^2 + 2 log t] ...

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  20. If f(pi) = 2 and int0^(pi) [f(x)+f^('')(x)] sin x dx = 5 then f(0)

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