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

If `I_(1)=int_(1-x)^(k) x sin{x(1-x)}dx` and `I_(2)=int_(1-x)^(k) sin{x(1-x)}dx`, then

A

`I_(1)2I_(2)`

B

`2I_(1)=I_(2)`

C

`I_(1)=I_(2)`

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. The values of 'a' for which int0^(a) (3x^(2)+4x-5)dx lt a^(3)-2 are

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  2. If (-1,2) and and (2,4) are two points on the curve y=f(x) and if g(x)...

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

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

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  5. If x=int(2)^(sint) sin^(-1) theta theta and y=int(n)^(sqrt(t))(sinthe...

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  6. |int(10)^(19) (sin x)/(1+x^(8))dx| is less than

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

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

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

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

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

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

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

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

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

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

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

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

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

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