Question 30 - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards
Last updated at Oct. 24, 2019 by Teachoo

Evaluate ∫ |x
^{
2
}
- 2x| dx from 1 to 3

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 โซ 3 1 |๐ฅ^2โ2๐ฅ| dx
|๐ฅ^2โ2๐ฅ|=|๐ฅ(๐ฅโ2)|
=|๐ฅ| |๐ฅโ2|
Thus, ๐ฅ=0, ๐ฅ=2
Since our integration is from 1 to 3, we ignore x = 0
โด |๐ฅ^2โ2๐ฅ|= {(๐ฅรโ(๐ฅโ2) ๐๐ 1โค๐ฅ<2๐ฅร(๐ฅโ2) ๐๐ 2โค๐ฅ<3)โค
|๐ฅ^2โ2๐ฅ|= {(โ(๐ฅ^2โ2๐ฅ) ๐๐ 1โค๐ฅ<2(๐ฅ^2โ2๐ฅ) ๐๐ 2โค๐ฅ<3)โค
Now,
โซ_1^3 |๐ฅ^2โ2๐ฅ| dx
= โโซ_1^2โ(๐ฅ^2โ2๐ฅ) ๐๐ฅ+โซ_2^3โ(๐ฅ^2โ2๐ฅ) ๐๐ฅ
= โโซ_1^2โ๐ฅ^2 ๐๐ฅ+โซ_1^2โ2๐ฅ ๐๐ฅ+โซ_2^3โ๐ฅ^2 ๐๐ฅโโซ_2^3โ2๐ฅ ๐๐ฅ
= โโซ_1^2โ๐ฅ^2 ๐๐ฅ+โซ_2^3โ๐ฅ^2 ๐๐ฅ+โซ_1^2โ2๐ฅ ๐๐ฅโโซ_2^3โ2๐ฅ ๐๐ฅ
= โ[๐ฅ^3/3]_1^2+[๐ฅ^3/3]_2^3+[๐ฅ^2 ]_1^2โ[๐ฅ^2 ]_2^3
= โ[2^3/3โ1^3/3]+[3^3/3โ2^3/3]+[2^2โ1^2 ]โ[3^2โ2^2 ]
= โ[8/3โ1/3]+[27/3โ8/3]+[4โ1]โ[9โ4]
= โ[7/3]+[19/3]+[3]โ[5]
= 12/3โ2
= 4โ2
= 2

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