Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise Revision Exercise Question 3 Maths Textbook Solution.

Answers (1)

best_answer

Answer: $\frac{16}{3}$

Given: $\int_{1}^{5} \frac{x}{\sqrt{2 x-1}} d x$

Hint: Let the denominator $(2x-1) = t$

Solution:

$\int_{1}^{5} \frac{x}{\sqrt{2 x-1}} d x$

Let $t=2 x-1=>x=\frac{t+1}{2}$

$dt = 2dx$ (differentiating w.r.t x)

$\begin{aligned} &I=\int_{1}^{5} \frac{t+1}{\frac{2}{\sqrt{t}}} \times \frac{d t}{2} \\ & \end{aligned}$

$I=\int_{1}^{5} \frac{t+1}{2 \sqrt{t}} d t=\frac{1}{4} \int_{1}^{5} \sqrt{t}+(t)^{\frac{-1}{2}} d t$

$=\frac{1}{4}\left(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}+\frac{t^{\frac{1}{2}}}{\frac{1}{2}}\right)_{1}^{5}$

$=\frac{1}{4}\left(\frac{2}{3}(2 x-1)^{\frac{3}{2}}+2(2 x-1)^{\frac{1}{2}}\right)_{1}^{5}$

$\begin{aligned} &=\frac{1}{4}\left(\frac{2}{3}(27-1)+2(3-1)\right) \\ & \end{aligned}$

$=\frac{1}{4}\left(\frac{2}{3}(26)+2(2)\right)$

$\begin{aligned} &=\frac{1}{4}\left(\frac{52+12}{3}\right) \\ & \end{aligned}$

$=\frac{1}{4} \times \frac{64}{3} \\$

$=\frac{16}{3}$

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

HD Video Lectures
Unlimited Mock Tests
Faculty Support

cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Board Economics Paper Analysis: 'Student-friendly', well balanced with moderate difficulty

anam-khan

CBSE Class 12 Hindi exam 2025 not postponed; special exam for those who miss

anam-khan

CBSE Board Exams 2025 LIVE: Class 12 Hindi paper over; updates on exam analysis, answer key

Latest Question