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Evaluate the following integrals: (1-...

Evaluate the following integrals: (1-35) `int_0^pixsinx cos^2x dx`

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The correct Answer is:
`(pi)/(3)`
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Evaluate the following integrals: (1-35) int0^pixsinx cos^2x dx

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  2. The integral int(pi//4)^(pi//2)(2 "cosec "x )^(17) dx is equal to

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  3. If for a real number y ,[y] is the greatest integral function less, th...

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  4. Let f(x) =x -[x] , for every real number x (where, [x] is integral par...

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  5. If g(x)=int(0)^(x)cos^(4)t dt, then g(x+pi) equals to (a)(g(x))/(g(pi)...

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  6. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)]dx , I2=i...

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  7. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

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  8. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

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  9. Let f: Rveca n dg: RvecR be continuous function. Then the value of the...

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  10. For any integer n,the integral overset(pi)underset(0)int e^(sin^(2)x)c...

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  11. Suppose we define integral using the following formula int(a)^(b)f(x)d...

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  12. Let the definite integral be defined by the formula int(a)^(b)f(x)dx=(...

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  13. Suppose we define integral using the following formula int(a)^(b)f(x)d...

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  14. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

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  15. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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  16. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

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  17. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

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  18. int(1)^(e^(37))(pisin(pilogx))/(x)dx equals to.

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

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  20. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

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  21. The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equ...

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