Chapter 7 Class 12 Integrals
Concept wise

Ex 7.6, 3 - Chapter 7 Class 12 Integrals

Last updated at December 16, 2024 by

Ex 7.6, 3 - Integrate x^2 e^x - Chapter 7 Class 12 NCERT

Ex 7.6, 3 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.6, 3 - Chapter 7 Class 12 Integrals - Part 3

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 5 questions, selected from your answers, mistakes, and progress.
Remove Ads Share on WhatsApp

Transcript

Ex 7.6, 3 Integrate the function š‘„^2 š‘’š‘„ āˆ«1ā–’怖š‘„^2 š‘’^š‘„ š‘‘š‘„怗 = š‘„^2 āˆ«1ā–’怖š‘’š‘„ š‘‘š‘„怗āˆ’āˆ«1ā–’(š‘‘(š‘„^2 )/š‘‘š‘„ āˆ«1ā–’怖š‘’š‘„ š‘‘š‘„怗) š‘‘š‘„ = š‘„^2. š‘’š‘„ āˆ’āˆ«1ā–’怖2š‘„ . š‘’š‘„怗 š‘‘š‘„ = š‘„^2. š‘’š‘„ āˆ’2āˆ«1ā–’怖š’™ . š’†š’™ć€— š’…š’™ Now we know that āˆ«1ā–’怖š‘“(š‘„) š‘”ā”(š‘„) 怗 š‘‘š‘„=š‘“(š‘„) āˆ«1ā–’š‘”(š‘„) š‘‘š‘„āˆ’āˆ«1ā–’(š‘“ā€²(š‘„)āˆ«1ā–’š‘”(š‘„) š‘‘š‘„) š‘‘š‘„ Putting f(x) = x2 and g(x) = ex ā€¦(1) Solving I1 āˆ«1ā–’怖š‘„ š‘’^š‘„ š‘‘š‘„怗 = š‘„āˆ«1ā–’š‘’š‘„ š‘‘š‘„āˆ’āˆ«1ā–’(š‘‘š‘„/š‘‘š‘„ āˆ«1ā–’š‘’^š‘„ š‘‘š‘„) š‘‘š‘„ = š‘„š‘’š‘„ āˆ’āˆ«1ā–’š‘’š‘„ š‘‘š‘„ = š‘„š‘’š‘„ āˆ’š‘’š‘„ Now we know that āˆ«1ā–’怖š‘“(š‘„) š‘”ā”(š‘„) 怗 š‘‘š‘„=š‘“(š‘„) āˆ«1ā–’š‘”(š‘„) š‘‘š‘„āˆ’āˆ«1ā–’(š‘“ā€²(š‘„)āˆ«1ā–’š‘”(š‘„) š‘‘š‘„) š‘‘š‘„ Putting f(x) = x and g(x) = ex Putting value of I1 in our equation āˆ“ āˆ«1ā–’怖š‘„^2 š‘’š‘„" " 怗 š‘‘š‘„" = " š‘„^2. š‘’š‘„ āˆ’2āˆ«1ā–’怖š’™ . š’†š’™ć€— š’…š’™ =š‘„^2. š‘’š‘„ āˆ’2(š’™š’†š’™āˆ’š’†^š’™ )+š¶ =š‘„^2. š‘’š‘„ āˆ’2š‘„š‘’š‘„+怖2š‘’怗^š‘„+š¶ =š’†š’™ (š’™^šŸāˆ’šŸš’™+šŸ)+š‘Ŗ

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo