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Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x...

Let `f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x` for all `x in (-pi/2,pi/2)` . Then the correct expression (s) is (are)

A

` int_(0)^(pi//4)xf(x) dx =(1)/(12)`

B

` int_(0)^(pi//4)f(x) dx =0`

C

` int_(0)^(pi//4)xf(x) dx =(1)/(6)`

D

` int_(0)^(pi//4)f(x) dx =(1)/(12)`

Text Solution

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The correct Answer is:
A, B
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

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  4. The option(s) with the values of aa n dL that satisfy the following eq...

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  5. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  7. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

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  8. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

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  9. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

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  10. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  11. Match the conditions/ expressions in Column I with statement in Column...

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  14. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  15. The value of int(In2)^(In3) (x sinx)dx is

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  16. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

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  17. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx is (are)

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  18. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^...

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  19. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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