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Definite integral of any discontinuous o...

Definite integral of any discontinuous or non diffrentiable function is normally done by the usage of the property`int_a^bf(x)dx=int_a^bf(x)dx+int_c^bf(x)dx`,where`c in(a,b)`,`int_1^(infty)[cosec^(-1)x]dx` (where[.] denotes greatest integer function)is equal to

A

1-cosec1

B

cosec1-1

C

1-sin1

D

none of these

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. If (2x)/piltsinxltx for 0ltxlt(pi/2), the the value of the integral in...

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  2. Definite integral of any discontinuous or non differentiable function ...

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  3. Definite integral of any discontinuous or non diffrentiable function i...

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  4. if m and M are the smallest and greatest values of a function f(x)defi...

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  5. if m and M are the smallest and greatest values of a function f(x) def...

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  6. let F(x)=int0^x(2t div1)/(t^2-2t+2)dt,x in[-1,1] then

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  8. I=int0^2x[2x]dx where [.] denotes the greatest integer function then t...

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  9. If pi/2ltalphalt(2pi)/3 and I=int 0^(sin2alpha)dx/sqrt(4cos^2alpha-x^2...

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  10. if int0^(x^2(1+x))f(t)dt=x then the value of 10f(2) must be

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  11. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

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  12. int(-pi//4)^(pi//4) (sec^2xdx)/(1+e^x)

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  13. Evaluateint0^(1)((x-1)/(x+1))^(1/2)dx

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  14. The value of (int0^n[x]dx)/(int0^n{x}dx is (where [x] and {x} denotes ...

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  15. Evaluate: int0^(pi/2)(sinx+cosx)^2/(1+sin2x)^(1/2)dx

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  16. Find the solution for x of the equation int(2^(1/2))^x1/(t(t^2-1)^(1/2...

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  17. If I1= inte^(e^2)dx/logx and I2= int1^2e^x/xdx, then find relation bet...

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  18. If int0^adx/(1+4x^2)= pi/8, then find the value of a.

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  19. Evaluate int0^(pi/2)(cosx)/(1+sinx)^2dx

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  20. Evaluate: int(pi/4)^((3pi)/4)dx/(1+cosx)

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