Home
Class 12
MATHS
If f (6-x ) =f (x), for all then 1/5 int...

If `f (6-x ) =f (x),` for all then `1/5 int _(2)^(3) x [f (x) + f (x+1)]dx` is equal to :

A

`int_3^4 f(x+2)dx`

B

`int_3^4 f(x+1)dx`

C

`int_1^2 f(x+1)dx`

D

`int_1^3 f(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=1/5 int_2^3 x[f(x)+f(x+1)]dx`…(i)
`I=1/5 int_2^3 (5-x) [f(5-x)+f(6-x)]dx`
`I=1/5 int_2^3 (5-x)[f(x+1)+f(x)]dx`…(ii)
Adding (i) and (ii)
`2I=5/5 int_2^3 [f(x)+f(x+1)]dx`
`2I=int_2^3 f(x) dx+ int_2^3 f(x+1)dx`
`2I=int_2^3 f(x)dx+int_2^3 f[6-x]dx`
`2I=int_2^3 f(x)dx+int_2^3 f(x)dx`
`I=int_2^3 f(x)dx rArr I=int_1^2 f(x+1)dx`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 11

    VMC MODULES ENGLISH|Exercise MATHEMATICS (Section-2)|5 Videos

  • MOCK TEST 10

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 12

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

int (f'(x))/( f(x) log(f(x)))dx is equal to

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

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

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx is equal to :

If f(a+b+1-x)=f(x) , for all x where a and b are fixed positive real numbers, the (1)/(a+b) int_(a)^(b) x(f(x)+f(x+1) dx is equal to :

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x in R . Then int_(-1//2)^(1//2) f(x+(1)/(2))sin x dx equals

The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to