Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 27

Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 27

Answers (1)

Answer:

10\left(\frac{\pi}{2}\right)^{9}

Hint:

To solve this equation we convert sin into cos.

Given:

I_{10}=\int_{0}^{\frac{\pi}{2}} x^{10} \sin x \; d x

Solution:
\begin{aligned} &I_{10}=\int_{0}^{\frac{\pi}{2}} x^{10} \sin x\; d x \\\\ &=-x^{10} \cdot \cos x-\int_{0}^{\frac{\pi}{2}} 10 x^{9} \cdot \cos x \; d x \end{aligned}

\begin{aligned} &=0-10 \int_{0}^{\frac{\pi}{2}} x^{9} \cdot \cos x \; d x \\\\ &=10\left[x^{9} \sin x-9 \int_{0}^{\frac{\pi}{2}} x^{8} \sin x \; d x\right]_{0}^{\frac{\pi}{2}} \end{aligned}

\begin{aligned} &=10\left(\frac{\pi}{2}\right)^{9}-90 \int_{0}^{\frac{\pi}{2}} x^{8} \sin x \; d x \\\\ &=10\left(\frac{\pi}{2}\right)^{9}-90 I_{8} \\\\ &=10\left(\frac{\pi}{2}\right)^{9} \end{aligned}

 

Posted by

infoexpert26

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 12th Computer Science Analysis 2026: Competency-based, direct questions, ‘easy’ MCQs; IP paper ‘balanced’
anam-khan

CBSE Class 12 Computer Science, IT, IP Exam 2026 LIVE: Question papers 'moderate', analysis updates
anam-khan

CBSE Board 12th Exams 2026 LIVE: Class 12 political science exam 'moderate' in difficulty; simple MCQs

Latest Question