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If int(-pi//3)^(pi//3) ((a)/(3)|tan x|+(...

If `int_(-pi//3)^(pi//3) ((a)/(3)|tan x|+(b tan x)/(1+sec x)+c)dx=0` where a, b, c are constants, then c=

A

a In 2

B

`(a)/(pi)`In 2

C

`-(a)/(pi)` In 2

D

`(2a)/(pi)` In 2`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 1
  1. If (-1,2) and and (2,4) are two points on the curve y=f(x) and if g(x)...

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  2. If I(1)=int(1-x)^(x) x sin{x(1-x)}dx and I(2)=int(1-x)^(x) sin{x(1-x)}...

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  3. If int(-pi//3)^(pi//3) ((a)/(3)|tan x|+(b tan x)/(1+sec x)+c)dx=0 wher...

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  4. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

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  5. The smallest interval [a,b] such that int0^(1) (1)/(sqrt(1+x^(4)))dx...

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  6. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

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

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  8. int(0)^(pi)(dx)/(1+3^(cos x)) is equal to:

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

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  10. Evaluate : int((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx

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

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

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

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

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

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

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

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

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  20. Let f(x) be a function satisfying f'(x)=f(x), f(0)=1 and g be a functi...

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