If f(2a-x)=-f(x), then show that, int(0)...

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

Answer

Step by step text solution for If f(2a-x)=-f(x), then show that, int_(0)^(2a)f(x)dx=0 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

DEFINITE INTEGRAL
CHHAYA PUBLICATION|Exercise EXERCISE 9B ( SHORT ANSWER TYPE QUESTIONS )|16 Videos
DEFINITE INTEGRAL
CHHAYA PUBLICATION|Exercise EXERCISE 9B ( LONG ANSWER TYPE QUESTIONS )|17 Videos
DEFINITE INTEGRAL
CHHAYA PUBLICATION|Exercise EXERCISE 9B ( MULTIPLE CHOICE TYPE QUESTIONS )|6 Videos
COORDINATE GEOMETRY
CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos
DEFINITE INTEGRAL AS AN AREA
CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Evaluate:If f(a-x)=f(x), then show that int_0^axf(x)dx=a/2int_0^af(x)dx

If f(x) and g(x) be continuous in the interval [0, a] and satisfy the conditions f(x)=f(a-x) and g(x)+g(a-x)=a , then show that int_(0)^(a)f(x)g(x)dx=(a)/(2)int_(0)^(a)f(x)dx . Hence find the value of int_(0)^(pi)xsinxdx .

Knowledge Check

If f(2a-x)=-f(x) then int_(0)^(2a)f(x)dx is equal to-

A

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

B

0

C

`int_(-a)^(a)f(x)dx`

D

1

If f(x)=|x-1| , then the value of int_(0)^(2)f(x) dx is -

A

2

B

0

C

1

D

-2

Similar Questions

Explore conceptually related problems

If f(x)=a+bx+cx^(2) , show that, int_(0)^(1)f(x)dx=(1)/(6)[f(0)+4f((1)/(2))+f(1)]

If f(x) is an odd function of x, then show that, int_(-a)^(a)f(x)dx=0 .

If f(2a-x)=-f(x), then overset(2a)underset(0)intf(x)dx =

If f(x)is integrable function in the interval [-a,a] then show that int_(-a)^(a)f(x)dx=int_(0)^(a)[f(x)+f(-x)]dx.

If f(x)=|x-1|+|x+1| , then evaluate int_(-2)^(2)f(x)dx .

If f(x) = -f(-x) then show that overset(a)underset(-a)int f(x)dx =0 .

CHHAYA PUBLICATION-DEFINITE INTEGRAL -EXERCISE 9B (VERY SHORT ANSWER TYPE QUESTIONS)

If f(2a-x)=-f(x), then show that, int(0)^(2a)f(x)dx=0
01:38
|
If f(x) is an odd function of x, then show that, int(-a)^(a)f(x)dx=0.
01:52
|
Evaluate : int(-1)^(1)|x|dx
02:56
|
Evaluate : int(-(pi)/(2))^((pi)/(2))|sinx|dx
01:36
|
Evaluate : int(1)^(3)|x-2|dx
04:46
|
Prove that, int(0)^(pi)f(sinx)dx=2int(0)^((pi)/(2))f(sinx)dx.
02:46
|
Show that, int(0)^(pi)xf(sinx)dx=(pi)/(2)int(0)^(pi)f(sinx)dx.
03:42
|
Show : int(a)^(b)f(kx)dx=(1)/(k)int(ka)^(kb)f(x)dx
03:22
|
Show : int(0)^((pi)/(2))sinxf(sin2x)dx=int(0)^((pi)/(2))cosxf(sin2x)...
02:31
|
Prove that, int(a)^(b)f(a+b-x)dx=int(a)^(b)f(x)dx.
02:49
|
int(0)^(pi)cos^(5)xdx=0
03:47
|
int(0)^(8pi)sin^(6)xdx=8int(0)^(pi)sin^(6)xdx
02:18
|
int(-a)^(a)(xe^(x^(4)))/(1+x^(2))dx=0
02:06
|
int(0)^(pi)sin^(3)xcos^(7)xdx=0
03:45
|
int(-(pi)/(2))^((pi)/(2))sin^(7)xdx=0
02:00
|
int(0)^(pi)(sin4theta)/(sintheta)d theta=0
08:11
|
int(0)^((pi)/(2))log(tanx)dx=0
02:21
|
int(0)^(2pi)sin^(4).(x)/(2)cos^(5).(x)/(2)dx=0
06:48
|
int(-a)^(a)xsqrt(a^(2)-x^(2))dx=0
02:17
|
int(-1)^(1)sin^(-1).(2x)/(1+x^(2))dx=0
06:43
|