If px is a cubic polynomial with p1-3- p0-2 and p-1-4- then -11 px d x isA- 2B- 3C- 4D- 5

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Quadratic Polynomial

If px is a cu...

Question

If p(x) is a cubic polynomial with p(1) = 3, p(0) = 2 and p (–1) = 4, then $\int_{- 1}^{1} p (x) d x$ is

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Solution

The correct option is D 5
$p (x) = a x^{3} + b x^{2} + c x + d$
p(0) = 2
d = 2
p(1) = 3
a + b + c + 2 = 3
a + b + c = 1 …………… (1)
p(-1) = 4
-a +b - c +2 =4
-a +b -c =2
from(1)and (2)
$2 b = 3 \Rightarrow b = \frac{3}{2} P (x) = a x^{3} + \frac{3}{2} x^{2} + c x + 2 \int_{- 1}^{1} p (x) d x = \int_{- 1}^{1} (a x^{2} + \frac{3}{2} x^{2} + c x + 2) d x = 5$

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If p(x) is a cubic polynomial with p(1) = 3, p(0) = 2 and p (–1) = 4, then ∫1−1p(x)dx is

The correct option is D 5p(x)=ax3+bx2+cx+d p(0) = 2 d = 2 p(1) = 3 a + b + c + 2 = 3 a + b + c = 1 …………… (1) p(-1) = 4 -a +b - c +2 =4 -a +b -c =2 from(1)and (2) 2b=3⇒b=32P(x)=ax3+32x2+cx+2∫1−1p(x)dx=∫1−1(ax2+32x2+cx+2)dx=5

If p(x) is a cubic polynomial with p(1) = 3, p(0) = 2 and p (–1) = 4, then $\int_{- 1}^{1} p (x) d x$ is