CBSE Class 12 Sample Paper for 2020 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## Evaluate ∫ |x 2 - 2x|  dx from 1 to 3

Note : - This is similar to Example 30 of NCERT – Chapter 7 Class 12

### Transcript

Question 30 Evaluate ∫ 3 1 |𝑥^2−2𝑥| dx |𝑥^2−2𝑥|=|𝑥(𝑥−2)| =|𝑥| |𝑥−2| Thus, 𝑥=0, 𝑥=2 Since our integration is from 1 to 3, we ignore x = 0 ∴ |𝑥^2−2𝑥|= {(𝑥×−(𝑥−2) 𝑖𝑓 1≤𝑥<2𝑥×(𝑥−2) 𝑖𝑓 2≤𝑥<3)┤ |𝑥^2−2𝑥|= {(−(𝑥^2−2𝑥) 𝑖𝑓 1≤𝑥<2(𝑥^2−2𝑥) 𝑖𝑓 2≤𝑥<3)┤ Now, ∫_1^3 |𝑥^2−2𝑥| dx = −∫_1^2▒(𝑥^2−2𝑥) 𝑑𝑥+∫_2^3▒(𝑥^2−2𝑥) 𝑑𝑥 = −∫_1^2▒𝑥^2 𝑑𝑥+∫_1^2▒2𝑥 𝑑𝑥+∫_2^3▒𝑥^2 𝑑𝑥−∫_2^3▒2𝑥 𝑑𝑥 = −∫_1^2▒𝑥^2 𝑑𝑥+∫_2^3▒𝑥^2 𝑑𝑥+∫_1^2▒2𝑥 𝑑𝑥−∫_2^3▒2𝑥 𝑑𝑥 = −[𝑥^3/3]_1^2+[𝑥^3/3]_2^3+[𝑥^2 ]_1^2−[𝑥^2 ]_2^3 = −[2^3/3−1^3/3]+[3^3/3−2^3/3]+[2^2−1^2 ]−[3^2−2^2 ] = −[8/3−1/3]+[27/3−8/3]+[4−1]−[9−4] = −[7/3]+[19/3]+[3]−[5] = 12/3−2 = 4−2 = 2

#### 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, Social Science, Physics, Chemistry, Computer Science at Teachoo.