Let f(x) be a polynomial of degree 2 sat...

Let f(x) be a polynomial of degree 2 satisfying `f(0)=1, f(0) =-2 and f''(0)=6`, then `int_(-1)^(2) f(x)` is equal to

A

6

B

2

C

9

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

C

Let `f(x)=ax^(2)+bx+c`. Then,
`f(0)=1 rArr c=1`
Now,
`f'(x)=2ax +b and f''(x)=2a`
`f'(0)=-2 and f''(09) =6 rArr b=-2 and a=3`
`:. f(x)=3x^(2)-2x+1`
`rArr underset(-1)overset(2)int f(x)dxunderset(-1)overset(2)int(3x^(2)-2x+1)dx=[ x^(3)-x^(2)+x]_(-1)^(2)`
`rArr underset(-1)overset(2)int f(x)dx=(8-4+2)-(-1-1-1)=9`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

DEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos
DEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|143 Videos
DEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos
CONTINUITY AND DIFFERENTIABILITY
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos
DERIVATIVE AS A RATE MEASURER
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) then f(4) equals

Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) then f(4) equals

If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then int_(0)^(1)x. f^''(2x) dx is equal to

Let f(x) be a polynomial of degree three f(0) = -1 and f(1) = 0. Also, 0 is a stationary point of f(x). If f(x) does not have an extremum at x=0, then the value of integral int(f(x))/(x^3-1)dx, is

If f(x) is a polynomial of degree four with leading coefficient one satisfying f(1)=1, f(2)=2,f(3)=3 .then [(f(-1)+f(5))/(f(0)+f(4))]

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 f'(x)=(1)/((1+x^(2))^(3//2)) and f(0)=0, then f(1) is equal to :

If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,....,f(n)=n/(n+1) , ,then the value of f (n+ 1) is

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x) , xleq0 and ((1+x)/(2+x))^(1/x) , xgt0 } Find g(x) such that f(x) is continuous and f'(1)=f(-1)

The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt0AAx in (0,1)

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs

The value of the integral int(a)^(a+pi//2) (|sin x|+|cosx|)dx is
Text Solution
|
If rArrI(n)= int(a)^(a+pi//2)(cos^(2)nx)/(sinx) dx, "then" I(2)-I(1),I...
Text Solution
|
Let f(x) be a polynomial of degree 2 satisfying f(0)=1, f(0) =-2 and f...
Text Solution
|
The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...
Text Solution
|
f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is
Text Solution
|
If f(x)= int0^(sinx) cos^(-1)t dt +int(0)^(cosx) sin^(-1)t dt, 0 lt ...
Text Solution
|
Let f(x) be a continous function such that int(m)^(n+1) f(x) dx =n^(3)...
Text Solution
|
Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...
Text Solution
|
If int(0)^(1) x e^(x^(2) ) dx=alpha int(0)^(1) e^(x^(2)) dx, then
Text Solution
|
If I=int(0)^(1) (1+e^(-x^2)) dx then, s
Text Solution
|
If I= int(0)^(1)(x)/(8+x^(3))dx then the smallest interval is which I ...
Text Solution
|
Letf :R rarr R be a continous function given by f(x+y)=f(x)f(y) "for a...
Text Solution
|
Let f beintegrable over [0,a] for any real value of a. If I(1)=int(0...
Text Solution
|
The value of underset(x rarr0)(lim)(2int(0)^(cos x ) cos^(-1) (t))/(2x...
Text Solution
|
If I(1)= int(1)^(sin theta) (x)/(1+x^(2)) dx and I(2) int(1)^("cosec" ...
Text Solution
|
If f(x)=int(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to
Text Solution
|
Let F(x) =f(x) +f((1)/(x)),"where" f(x)=int(1)^(x) (log t)/(1+t) dt Th...
Text Solution
|
int(0)^(x) (bt cos 4t-a sin 4t)/(t^(2))dt=(a sin 4x)/(x) "foe all "x ...
Text Solution
|
Let f:RtoR,f(x)={:(|x-[x]|,[x] "is odd"),(|x-[x+1]|,[x] "is even"):} w...
Text Solution
|
If f(x) = sin x+cos x and g(x) = {:{((|x|)/(x),","x ne0),(2,","x=0):} ...
Text Solution
|