Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise18.5 Question 2 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise18.5 Question 2 Maths Textbook Solution.

Answers (1)

Answer:  \frac{2}{5}(x+2)^{\frac{5}{2}}-\frac{6}{3}(x+2)^{\frac{1}{2}}+C

Hint: Let u= x+2

Given: \int x\sqrt{x+2}dx

Solution:

Let u= x+2

\frac{du}{dx}= 1

Applying the substitution we have:

\begin{aligned} &I=\int(u-2) \sqrt{u} d u \\ &\therefore I=(u-2) u^{\frac{1}{2}} d u \\ &=\int u^{\frac{3}{2}}-2 u^{\frac{1}{2}} d u \end{aligned}
\begin{aligned} &\therefore I=\frac{u^{\frac{5}{2}}}{\frac{5}{2}}-\frac{2 u^{\frac{3}{2}}}{\frac{3}{2}}+C \\ &\therefore I=\frac{2}{5} u^{\frac{5}{2}}-\frac{4}{3} u^{\frac{3}{2}}+C \\ &\therefore I=\frac{2}{5}(x+2)^{\frac{5}{2}}-\frac{4}{3}(x+2)^{\frac{3}{2}}+C \end{aligned}

 

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question