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If pi/2ltalphalt(2pi)/3 and I=int 0^(sin...

If `pi/2ltalphalt(2pi)/3` and `I=int _0^(sin2alpha)dx/sqrt(4cos^2alpha-x^2)` then the value of `(I+alpha)/pi`must be

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. int(-pi/3)^(pi/3) ((xsinx)dx)/(cos^2x) is

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  16. The value of int(-3)^3(ax^5+bx^3+cx+k)dx where a,b, c, k are constant ...

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  17. int(-pi/2)^(pi/2) sinabs(x) dx is equal to

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  18. If f(x) is defined on [2,2] by f(x) =4x^2-3x+1 and g(x) =(f(-x)-f(x))/...

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  19. I= int(-pi)^(pi) (e^sinxdx)/(e^sinx +e^(-sinx) then I equals

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  20. If I= int0^(100pi) sqrt(1-cos2x)dx then the value I is :

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