Ā
Example 25 (iii) - Chapter 7 Class 12 Integrals
Last updated at December 16, 2024 by Teachoo
Examples
Example 1 (i)
You are here
You are here
Chapter 7 Class 12 Integrals
Serial order wise
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.
Transcript
Example 25 Evaluate the following integrals: (iii) ā«_1^2ā(š„ šš„)/((š„ + 1) (š„ + 2) ) šš„ š¹(š„)=ā«1ā(š„ šš„)/(š„ + 1)(š„ + 2) We can write the integrate as : š„/(š„ + 1)(š„ + 2) =A/(š„ + 1)+B/(š„ + 2) š„/(š„ + 1)(š„ + 2) =(A(š„ + 2) + B(š„ + 1))/(š„ + 1)(š„ + 2) Canceling denominators š„=A(š„+2)+B(š„+1) Putting š=āš ā2=A(2+2)+B(2+1) ā2=A Ć0+B(ā1) ā2=āB B=2 Putting š=āš ā1=A(ā1+2)+B(ā1+1) ā1=A(1)+B(0) ā1=A A=ā1 =āššš|š„+1|+ššš|š„+2|^2 =ššš|š„+2|^2āššš|š„+1| =ššš|(š„ + 2)^2/(š„ + 1)| Hence š¹(š„)=ššš|(š„ + 2)^2/(š„ + 1)| Now, ā«_1^2āćš„/(š„ + 1)(š„ + 2) šš„ć=š¹(2)āš¹(1) ā«_1^2āćš„/(š„ + 1)(š„ + 2) šš„ć=ššš|(2 + 2)^2/(2 + 1)|āššš|(1 + 2)^2/(1 + 1)| =ššš|(4)^2/3|āššš|(3)^2/2| =ššš|(4^2/3)/(3^2/2)| =ššš|4^2/3 Ć 2/3^2 | =ššš|16/3 Ć 2/9| =ššš|32/27 | =š„šØš ā”(šš/šš)
