CBSE Class 12 Sample Paper for 2020 Boards
You are here
CBSE Class 12 Sample Paper for 2020 Boards
Last updated at July 21, 2026 by Teachoo
Note : - This is similar to Example 30 of NCERT – Chapter 7 Class 12
Check the answer here https://www.teachoo.com/4811/727/Example-30---Evaluate-integral--1----2--x3---x--dx/category/Examples/
Transcript
Question 30 Evaluate ā« 3 1 |š„^2ā2š„| dx |š„^2ā2š„|=|š„(š„ā2)| =|š„| |š„ā2| Thus, š„=0, š„=2 Since our integration is from 1 to 3, we ignore x = 0 ā“ |š„^2ā2š„|= {(š„Ćā(š„ā2) šš 1ā¤š„<2š„Ć(š„ā2) šš 2ā¤š„<3)ā¤ |š„^2ā2š„|= {(ā(š„^2ā2š„) šš 1ā¤š„<2(š„^2ā2š„) šš 2ā¤š„<3)ā¤ Now, ā«_1^3 |š„^2ā2š„| dx = āā«_1^2ā(š„^2ā2š„) šš„+ā«_2^3ā(š„^2ā2š„) šš„ = āā«_1^2āš„^2 šš„+ā«_1^2ā2š„ šš„+ā«_2^3āš„^2 šš„āā«_2^3ā2š„ šš„ = āā«_1^2āš„^2 šš„+ā«_2^3āš„^2 šš„+ā«_1^2ā2š„ šš„āā«_2^3ā2š„ šš„ = ā[š„^3/3]_1^2+[š„^3/3]_2^3+[š„^2 ]_1^2ā[š„^2 ]_2^3 = ā[2^3/3ā1^3/3]+[3^3/3ā2^3/3]+[2^2ā1^2 ]ā[3^2ā2^2 ] = ā[8/3ā1/3]+[27/3ā8/3]+[4ā1]ā[9ā4] = ā[7/3]+[19/3]+[3]ā[5] = 12/3ā2 = 4ā2 = 2
