Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Evaluate the integrals in Exercises 1 to 8 using substitution. (1/x - 1/ 2x^2)

Evaluate the integrals in Exercises 1 to 8 using substitution.

    Q8.    \int_1^2\left(\frac{1}{x} - \frac{1}{2x^2} \right )e^{2x}dx

Answers (1)

best_answer

\int_1^2\left(\frac{1}{x} - \frac{1}{2x^2} \right )e^{2x}dx
let 2x =t \Rightarrow 2dx =dt
when x = 1 then t = 2 and when x = 2 then t= 4

\\=\frac{1}{2}\int_{2}^{4}(\frac{2}{t}-\frac{2}{t^2})e^tdt\\
let
 \frac{1}{t} = f(t)\Rightarrow f'(t)=-\frac{1}{t^2}
\Rightarrow \int_{2}^{4}(\frac{1}{t}-\frac{1}{t^2})e^tdt =\int_{2}^{}4e^t[f(t)+f'(t)]dt
                                          \\=[e^tf(t)]^4_2\\ =[e^t.\frac{1}{t}]^4_2\\ =\frac{e^4}{4}-\frac{e^2}{2}\\ =\frac{e^2(e^2-2)}{4}
                                        

Posted by

manish

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 history paper 2025 moderately difficult, tested students’ understanding
anam-khan

CBSE Class 12 Computer Science Exam Analysis 2025: Paper 'moderate', but 'tougher' than last three years
anam-khan

CBSE Class 12 Accountancy Exam Analysis 2025: Paper ‘moderate', includes application-based questions

Latest Question