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Let f(x) be an integrable function defined on [a,b],`b gt a gt 0`. If `I_(1)=int_(pi//6)^(pi//3) f(tan theta+cos theta)sec^(2) theta d theta` and,
`I_(2)=int_(pi//6)^(pi//3) f(tan theta +cot theta)cosec^(2) theta d theta`, then `(I_(1))/(I_(2))=`

A

a positive integer

B

a negative integer

C

an irrational number none of these

D

none of these

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A
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

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  2. If f(x)=int(0)^(x) sin^(4)t dt, then f(x+2pi) is equal to

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  3. int(0)^(pi) (1)/(1+3^(cosx)) dx is equal to

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  4. Let int(0)^(a) f(x)dx=lambda and int(0)^(a) f(2a-x)dx=mu. Then, int(...

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  5. The value of int(pi//4)^(3pi//4) (x)/(1+sin x) dx is equal to

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  6. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

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  7. The value of int(-1)^(1) max[2-x,2,1+x] dx is

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  8. int(0)^(pi//4) sin(x-[x]) dx is equalto

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  9. The value of the integral int(-1)^(1) (x-[2x])dx,is

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  10. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

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  11. Let f:R in R be a continuous function such that f(x) is not identicall...

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  12. Let f(x)=int(0)^(x) |xx-2|dx, ge 0. Then, f'(x) is

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  13. Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, is equal to (A) k/e (B) e/k (C)...

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  14. Let f(x) be an integrable function defined on [a,b],b gt a gt 0. If I(...

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  15. int(0)^(sqrt(2)) [x^(2)]dx, is

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  16. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a...

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  17. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

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  18. If f(y)=e^(y)=e^(y),g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y) dy, ...

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  19. If I(n)=int(0)^(pi//2) x^(n) sin x dx, then I(4)+12I(2) is equal to\

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  20. int(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

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