Home
Class 12
MATHS
Let p(x) be a function defined on R such...

Let `p(x)` be a function defined on `R` such that `p'(x)=p'(1-x)` for all `x epsilon[0,1],p(0)=1` and `p(1)=41`.
Then `int_(0)^(1)p(x)dx` is equals to (a)`42` (b)`sqrt(41)` (c)`21` (d)`41`

A

`42`

B

`sqrt(41)`

C

`21`

D

`41`

Text Solution

Verified by Experts

The correct Answer is:
C
`p'(x)=p'(1-x)`
`impliesp(x)=-p(1-x)+c`
At `x=0`
`p(0)=-p(1)+cimplies42=c`
`:.p(x)=-p(1-x)+42`
`impliesp(x)+p(1-x)=42`
`I=int_(0)^(1)p(x)dx=int_(0)^(1)p(1-x)dx`
`:. 2I=int_(0)^(1)(p(x)+p(1-x))dx=int_(0)^(1)(42)dx`
`impliesI=21`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE ADVANCED|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise NUMERICAL VALUE_TYPE|28 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Let p(x) be a function defined on R such that p '(x)""=""p '(1-x) , for all x in [0,""1],""p(0)""=""1 and p(1)""=""41 . Then int_0^1p(x)dx equals (1) 21 (2) 41 (3) 42 (4) sqrt(41)

Let p(x) be a function defined on R such that lim_(xrarr infty) f (3x)/(f(x))=1,p'(x)=p'(1-x),"for all" x in [0,1],p(0)=1 and p(1)=41."Then" , int_(0)^(1)p(x) dx equals

Let P(x) be a polynomial of degree 11 such that P(x) = (1)/(x + 1) for x = 0, 1, 2, 3,"…."11 . The value of P(12) is.

P(x) is a non-zero polynomial such that P(0)=0 and P(x^3)=x^4P(x),P'(1)=7 and int_0^1P(x)=1.5 then int_0^1P(x) P'(x) dx =

Let p=lim_(xto0^(+))(1+tan^(2)sqrt(x))^((1)/(2x)) . Then log_(e)p is equal to

If P(x) is a polynomial such that P(x^(2)+1)={P(x)}^(2)+1 and P(0)=0, then P'(0) is equal to

l_(1)=int2^(x)dx=p(x)+c_(1)andl_(2)=int((1)/(2))^(x)dx=m(x)+c_(1) then p(x)-m(x) is equal to

Let p (x) be a polynomial with real coefficient and p (x)-p'(x) =x^(2)+2x+1. Find P (-1).

The function 'f' is defined by f(x)=x^p(1-x)^q for all x\ in R , where p ,\ q are positive integers, has a maximum value, for x equal to : (p q)/(p+q) (b) 1 (c) 0 (d) p/(p+q)

If cos^(-1)((1-x^(2))/(1+x^(2)))+sin^(-1)((2x)/(1+x^(2)))=p for all x in[-1,0] , then p is equal to