First slide

Evaluation of definite integrals

Question

A polynomial $P$ is positive for $x > 0,$ and the area of the region bounded by $P (x),$ the x-axis, and the vertical lines $x = 0$ and $x = K$ is $K^{2} (K + 3) / 3$ .The polynomial $P (x)$ is

Moderate

A

$x^{2} + 2 x$
B

$x^{2} + x + 1$
C

$x^{2} + 2 x + 1$
D

$x^{3} + 1$

Solution

We have $\int_{0}^{K} P (t) d t = \frac{K^{2} (K + 3)}{3}$ Differentiating
$w . r . t K,$ we get $P (K) = \frac{K^{2}}{3} + \frac{2 K}{3} (K + 3) = K^{2} + 2 K$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App