First slide

Evaluation of definite integrals

Question

$\frac{d}{dx} (\int_{x^{2}}^{x^{3}} \frac{1}{\log t} dt)$ is equal to

Moderate

A

$\frac{1}{\log x}$
B

$\frac{x^{2}}{\log x}$
C

$\frac{x^{2} - x}{\log x}$
D

None of these

Solution

$\begin{array}{l} \frac{d}{dx} (\int_{x^{2}}^{x^{3}} \frac{1}{\log t} \cdot dt) = \frac{1}{\log x^{3}} \cdot \frac{d}{dx} (x)^{3} - \frac{1}{\log x^{2}} \cdot \frac{d}{dx} (x^{2}) \\ = \frac{3 x^{2}}{3 \log x} - \frac{2 x}{2 \log x} \\ \Rightarrow \frac{d}{dx} (\int_{x^{2}}^{x^{3}} \frac{1}{\log t} dt) = \frac{1}{\log x} \cdot (x^{2} - x) \end{array}$

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