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Let a function `f` be even and integrable everywhere and periodic with period 2. Let `g(x)=int_0^x f(t) dt` and `g(t)=k`For what value of g in terms of k is

A

`g(2n) = 0` for every integer n

B

`g(x)` is an even function

C

`g(x)` and `f(x)` have the same period

D

`g(x)` is an odd function

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A, B, C
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
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  2. If I = int(0)^(2pi)sin^(2)xdx, then

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  3. Let a function f be even and integrable everywhere and periodic with p...

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  4. Let f : R rarr R be defined as f(x) = int(-1)^(e^(x)) (dt)/(1+t^(2)) +...

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  5. If a,b in R^(+) then find Lim(nrarroo) sum(k=1)^(n) ( n)/((k+an)(k+bn...

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  6. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

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  7. If f(x) in inegrable over [1,2] then int(1)^(2) f(x) dx is equal to :

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  8. Let I(n) = underset(0)overset(1//2)int(1)/(sqrt(1-x^(n))) dx where n ...

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  9. If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then wh...

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  10. Let f(x) = int(0)^(x)|2t-3|dt, then f is

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  11. Let f(x) = int(0)^(pi)(sinx)^(n) dx, n in N then

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  12. Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R, then

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  13. Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then

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  14. Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...

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  15. Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then

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  16. Let f(a,b) = int(a)^(b)(x^(2)-4x+3)dx, (bgt 0) then

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  17. Let I = int(2)^(oo)((2x)/(x^(2)+1)- (1)/(2x+1)) dx & I is a finite r...

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  18. Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...

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  19. lim(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."...

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  20. Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...

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