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Evaluate: int0^2[x^2-x+1]dx ,w h e r e[d...

Evaluate: `int_0^2[x^2-x+1]dx ,w h e r e[dot]` denotos the greatest integer function.

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  8. The value of the definite integral, int0^(pi/2) (sin5x)/sinx dx is

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  9. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, n in I (a) pi/2 ...

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  10. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

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  11. If In=int0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ...

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  12. int0^1(tan^(-1)x)/x dx is equals to (a) int0^(pi/2)(sinx)/x dx (b)...

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  13. If int0^1(sint)/(1+t)dt=alpha, then the value of the integral int(4pi-...

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  14. L e tI1=int0^1(e^xdx)/(1+x) a n dI2=int0^1(x^2dx)/(e^(x^3)(2-x^3))dot ...

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  15. int(sintheta)^(costheta)f(xtantheta)dx(w h e r etheta!=(npi)/2,n in I...

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  16. Let g(x)=int0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,...

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  17. The value of int0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (...

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  18. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)"is equal to" (a) 3/...

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  19. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

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  20. For any real number x, let [x] denote the largest integer less than or...

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