First slide

Evaluation of definite integrals

Question

$\int (1 + 2 x + 3 x^{2} + 4 x^{3} + - - - -) d x where 0 < | x | < 1$

Moderate

A

$\frac{1}{1 - x} + c$
B

$\frac{2}{3 {(1 - x)}^{2}} + c$
C

$4 {(1 - x)}^{3} + c$
D

$(1 - x) + c$

Solution

let
$\begin{array}{l} S = 1 + 2 x + 3 x^{2} + 4 x^{3} + - - - \\ \frac{x S = x + 2 x^{2} + 3 x^{3} + - - -}{(1 - x) S = 1 + x + x^{2} + x^{3} + - - -} \\ (1 - x) S = \frac{1}{1 - x} \\ S = \frac{1}{(1 - x)^{2}} \\ S = (1 - x)^{- 2} \\ ∴ \int (1 + 2 x + 3 x^{2} + - - - -) d x \\ = \int (1 - x)^{- 2} d x = \frac{(1 - x)^{- 1}}{(- 1) (- 1)} + c \\ = (1 - x)^{- 1} + c \end{array}$

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