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If P(x) is a cubic polynomial with P(1)=...

If P(x) is a cubic polynomial with P(1)=3,P(0)=2 and P(-1)=4, then `underset(-1)overset(1)fP(x)dx` is

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
`Let P(x)-ax^(3)+bx^(2)+cx+d`
a+b+c+d=3
d=2
-a+b-c+d4
2b+2d=7
2b+4=7
2b=3
`b=(3)/(2)`
`underset(-1)overset(1)(f)(ax^(3)+bx^(2)+cx+d)dx`
`2underset(0)overset(1)(f)(bx^(2)+d)dx`
`=2((b)/(3)+d)`
`=2((1)/(2)+2)=5`
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