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The value of the integral int(pi//6)^(pi...

The value of the integral `int_(pi//6)^(pi//3)(dx)/(1+tan^(5)x)` is

A

1

B

`pi//12`

C

`pi//6`

D

none of these

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Statement I: The value of the integral int_(pi//6)^(pi//3) (dx)/(1+sqrt(tanx)) is equal to (pi)/6 . Statement II: int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

Statement-1: The value of the integral int_(pi//6)^(pi//3) (1)/(sqrt(tan)x)dx is equal to (pi)/(6) Statement-2: int_(a)^(b) f(x)dx=int_(a)^(b) f(a+b-x)dx

Statement I The value of the integral int_(pi//6)^(pi//3) (dx)/(1+sqrt(tan x)) is pi/6 Statement II int_(a)^(b) f(x) dx = int_(a)^(b) f(a+b-x)dx

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FIITJEE-DEFINITE INTEGRAL -ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-I)
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  3. The value of the integral int(pi//6)^(pi//3)(dx)/(1+tan^(5)x) is

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  4. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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  5. The value of int(0)^(pi//2)ln((sin^(2)theta)/(cos^(3)theta))d theta is

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  6. int(-1)^(1)[tan^(-1){sin(cos^(-1)x)}+cot^(-1){cos(sin^(-1)x)}dx=

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  7. int- 8^8(sin^(93)x+x^(295))\ dx

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  9. int0^100 {sqrtx} dx (where {x) is fractional part of x ) =

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  10. int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=

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  11. If bgta, then int(a)^(b)(dx)/(sqrt((x-a)(b-x))) is equal to

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  12. inta^bsqrt((x-a)(b-x)) dx , a > b

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  13. Let f(x)=int(1)^(x)t(t^(2)-3t+2)dt,1lexle4. Then the range of f (x) is

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  14. Suppose g(x) satisfies g(x)=x+int(0)^(1)(xy^(2)+yx^(2))g(y)dy, then g(...

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  15. For x epsilonR, and a continuous function f let I(1)=int(sin^(2)t)^(1+...

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  17. If f(x)=f(a+b-x), then overset(b)underset(a)int xf(x)dx is equal to

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  18. If f(x)=int((1)/(x))^(sqrt(x))cost^(2)dt(xgt0)" then "(df(x))/(dx) is

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  19. Let f(x) = 1/x ln(x/e^x) then its primitive w.r.t x is

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  20. The greatest value of f(x)=int1^x|t|\ dt on the interval [-1/2,1/2] :

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