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If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx...

If `int_(0)^(2a) f(x)dx=int_(0)^(2a) f(x)dx`, then

A

`f(2a-x)=-f(x)`

B

`f(2a-x)=f(x)`

C

f(x) is an odd function

D

f (x) is an even function

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The correct Answer is:
B
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If : int_(0)^(2a)f(x)dx=2.int_(0)^(a)f(x)dx , then :

int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=

int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=

int_(0)^(a)f(x)dx=

int_(0)^(a)f(x)dx

Prove that : int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x)dx hence evaluate : int_(0)^(pi//2) (sin x)/(sin x + cos x) dx

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

Prove that int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx . Hence find int_(0)^((pi)/(2)) sin^(2) xdx

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

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  2. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

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  3. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

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  4. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

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  5. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

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  6. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

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  7. The value of the integral int 0^oo 1/(1+x^4)dx is

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  8. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

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  9. The value of alpha in [0,2pi] which does not satify the equation int(p...

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  10. lim(x to 0)(int(0)^t(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

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  11. If x satisfies the equation x^(2)( int(0)^(1) (dt)/(t^(2)+ 2t cos al...

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  12. The value of alpha in (-pi, 0) satisfying sin alpha+int(alpha)^(2alpha...

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  13. The value of int(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx i...

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  14. The value of int(0)^(pi) (1)/(5+3cosx)dx, is

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  15. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  16. lim(n to oo) sum(r=1)^(n) {(r^(3))/(r^(4)+n^(4))} equals

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  17. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  18. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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  19. The solution of the equation int(0)^(x) (1)/(xsqrt(2^(2)-1))dx=(pi)/(1...

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  20. Let I(n)=int(0)^(pi//4) tan^(n) x dx, (n gt1 and n in N), then

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