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(sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)d...

`(sum_(n=1)^10int_(-2n-1)^(-2n)sin^(27)(x)dx+sum_(n=1)^10int_(2n)^(2n+1)sin^(27)(x)dx)`

A

`27^(2)`

B

-54

C

54

D

0

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 1
  1. The smallest interval [a,b] such that int0^(1) (1)/(sqrt(1+x^(4)))dx...

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

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

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

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

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

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

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

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

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

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

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

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

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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), f(0)=1 and g be a functi...

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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),g(y)=y,ygt0 and F(t)=int(0)^(1)f(t-y)g(y)dt then

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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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