First slide

Methods of integration

Question

If the variables $x$ and $y$ are related by the equation
$x = \int_{0}^{y} \frac{d x}{\sqrt{1 + 9 x^{2}}}$ and $\frac{d^{2} y}{d x^{2}}$ is proportional to y then
the constant of proportionality is

Moderate

A

4
B

6
C

5
D

9

Solution

$\frac{d x}{d y} = \frac{1}{\sqrt{1 + 9 y^{2}}} \to \frac{d y}{d x} = \sqrt{1 + 9 y^{2}}$
$\frac{d^{2} y}{d x^{2}} = \frac{1}{2} \frac{18 y}{\sqrt{1 + 9 y^{2}}} \frac{d y}{d x} = 9 y$ . Thus the constant of
proportionality is equal to 9.

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