Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide Solutio for RD Sharma Class 12 Chapter Indefinite Integrals Exercise 18.12 Question 9

Provide Solutio for RD Sharma Class 12 Chapter Indefinite Integrals Exercise 18.12 Question 9

Answers (1)

best_answer

Answer: - -\frac{1}{6} \cos ^{6} x+\frac{1}{8} \cos ^{8} x+C

Hint: - Use substitution method to solve this integral.

Given: -\int \sin ^{3} x \cdot \cos ^{5} x d x

Solution: - Let   I=\int \sin ^{3} x \cdot \cos ^{5} x d x

Substitute \cos x=t \Rightarrow-\sin x d x=d t then

\begin{aligned} I &=\int\sin ^{3} x t^{5} \cdot \frac{d t}{-\sin x}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \left [ \because \cos x=t \right ] \\ &=-\int \sin ^{2} x t^{5} \cdot d t=-\int\left(t-\cos ^{2} x\right) t^{5} d t \quad \quad \quad \quad \quad \quad \quad \left [ \because \sin ^{2}x+\cos ^{2 }x=1 \right ]\\ &=-\int\left(1-t^{2}\right)\left(t^{5}\right) d t=-\int\left(t^{5}-t^{5} t^{2}\right) d t \end{aligned}
    \begin{aligned} &=-\int\left(t^{5}-t^{7}\right) d t=-\int t^{5} d t+\int t^{7} d t \\ &=-\frac{t^{5+1}}{5+1}+\frac{t^{7+1}}{7+1}+C \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+C\right] \\ &=-\frac{t^{6}}{6}+\frac{t^{8}}{8}+c=-\frac{\cos ^{6} x}{6}+\frac{\cos ^{8} x}{8}+C \quad\quad\quad\quad\quad\quad\quad[\because \cos x=t] \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

CBSE Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in
anam-khan

CBSE Board 2025: Class 10th, 12th supplementary date sheet out; exams from July 15
anam-khan

CBSE issues final reminder to schools for supplementary exam LOC submission; submit by today without late fee

Latest Question