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If I = int(0)^(2pi)sin^(2)xdx, then...

If `I = int_(0)^(2pi)sin^(2)xdx`, then

A

`I=4overset(pi)underset(0)int sin^(2)x" dx"=4overset(pi//2)underset(0)int sin^(2)x" dx"`

B

`I=overset(pi//2)underset(0)intcos^(2)x" dx"`

C

`I=8overset(pi//4)underset(0)int sin^(2)x" dx"`

D

none of these

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. The value of the integral int(0)^(3) sqrt(3+x^(3))dxlies in the inter...

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  2. The value of the integral int(0)^(1) (1)/((1+x^(2))^(3//2))dx is

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  3. If I = int(0)^(2pi)sin^(2)xdx, then

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  4. If int(0)^(1) f(x)=M,int(0)^(1) g(x)dx=N, then which of the following ...

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  5. The value of int( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

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  6. The value of int(-pi//2)^(pi//2) sin{log(x+sqrt(x^(2)+1)}dx is

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  7. The value of int(0)^(2pi) cos^(99)x dx, is

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  8. If f(a+x)=f(x), then int(0)^(na) f(x)dx is equal to (n in N)

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  9. If f(t) is an odd function, then prove that varphi(x)=inta^xf(t)dt is ...

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  10. If f(x) is an integrable function over every interval on the real line...

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  11. If I(1)=int(3pi)^(0) f(cos^(2)x)dx and I(2)=int(pi)^(0) f(cos^(2)x) th...

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  12. If f(x) is a quadratic polynomial in x such that 6int0^1 f(x)dx-{f(0...

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  13. The value of integral int(-2)^(4) x[x]dx is

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  14. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

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  15. Given that, F(x)=(1)/(x^(2))int(4)^(x)(4t^(2)-2F'(t))dt, find F'(4).

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  16. It is known that f(x) is an odd function in the interval [p/2, p/2] an...

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  17. Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2...

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  18. int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to

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  19. The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is

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  20. The value of int(-1)^(1)(x|x|)dx is equal to

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