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If f(x)=int(0)^(x) sin^(4)t dt, then f(x...

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

A

f(x)

B

`f(x)+f(2pi)`

C

`gf(x)-f(2pi)`

D

`f(x).f(2pi)`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-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) (1)/(1+3^(cosx)) dx 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(...

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

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

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

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

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

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

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