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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 March 23, 2023 by

Evaluate ∫ |x 2 - 2x|  dx from 1 to 3

Evaluate Integral |x^2 - 2x| from 1 to 3 - Teachoo - CBSE Class 12 Sam

Question 30 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2
Question 30 - CBSE Class 12 Sample Paper for 2020 Boards - Part 3

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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/

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Transcript

Question 30 Evaluate ∫ 3 1 |π‘₯^2βˆ’2π‘₯| dx |π‘₯^2βˆ’2π‘₯|=|π‘₯(π‘₯βˆ’2)| =|π‘₯| |π‘₯βˆ’2| Thus, π‘₯=0, π‘₯=2 Since our integration is from 1 to 3, we ignore x = 0 ∴ |π‘₯^2βˆ’2π‘₯|= {(π‘₯Γ—βˆ’(π‘₯βˆ’2) 𝑖𝑓 1≀π‘₯<2π‘₯Γ—(π‘₯βˆ’2) 𝑖𝑓 2≀π‘₯<3)─ |π‘₯^2βˆ’2π‘₯|= {(βˆ’(π‘₯^2βˆ’2π‘₯) 𝑖𝑓 1≀π‘₯<2(π‘₯^2βˆ’2π‘₯) 𝑖𝑓 2≀π‘₯<3)─ Now, ∫_1^3 |π‘₯^2βˆ’2π‘₯| dx = βˆ’βˆ«_1^2β–’(π‘₯^2βˆ’2π‘₯) 𝑑π‘₯+∫_2^3β–’(π‘₯^2βˆ’2π‘₯) 𝑑π‘₯ = βˆ’βˆ«_1^2β–’π‘₯^2 𝑑π‘₯+∫_1^2β–’2π‘₯ 𝑑π‘₯+∫_2^3β–’π‘₯^2 𝑑π‘₯βˆ’βˆ«_2^3β–’2π‘₯ 𝑑π‘₯ = βˆ’βˆ«_1^2β–’π‘₯^2 𝑑π‘₯+∫_2^3β–’π‘₯^2 𝑑π‘₯+∫_1^2β–’2π‘₯ 𝑑π‘₯βˆ’βˆ«_2^3β–’2π‘₯ 𝑑π‘₯ = βˆ’[π‘₯^3/3]_1^2+[π‘₯^3/3]_2^3+[π‘₯^2 ]_1^2βˆ’[π‘₯^2 ]_2^3 = βˆ’[2^3/3βˆ’1^3/3]+[3^3/3βˆ’2^3/3]+[2^2βˆ’1^2 ]βˆ’[3^2βˆ’2^2 ] = βˆ’[8/3βˆ’1/3]+[27/3βˆ’8/3]+[4βˆ’1]βˆ’[9βˆ’4] = βˆ’[7/3]+[19/3]+[3]βˆ’[5] = 12/3βˆ’2 = 4βˆ’2 = 2

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