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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 Dec. 16, 2024 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 ∫ 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
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

    3. CBSE Class 12 Sample Paper for 2020 Boards

    CBSE Class 12 Sample Paper for 2019 Boards →
CBSE Class 12 Sample Paper for 2019 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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