First slide

Evaluation of definite integrals

Question

If $l (m, n) = \int_{0}^{1} t^{m} (1 + t)^{n} d t$ then the expression for $l (m, n)$ in terms of $l (m + 1, n - 1)$ is

Moderate

A

$\frac{2^{n}}{m + 1} - \frac{n}{m + 1} l (m + 1, n - 1)$
B

$\frac{n}{m + 1} l (m + 1, n - 1)$
C

$\frac{2^{n}}{m + 1} + \frac{n}{m + 1} l (m + 1, n - 1)$
D

$\frac{m}{n + 1} l (m + 1, n - 1)$

Solution

${I (m, n) = \frac{1}{m + 1} t^{m + 1} (1 + t)^{n}]}_{0}^{1}$
$\begin{array}{l} - \frac{n}{m + 1} I (m + 1, n - 1) \\ \Rightarrow I (m, n) = \frac{2^{n}}{m + 1} - \frac{n}{m + 1} I (m + 1, n - 1) \end{array}$

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