CBSE Class 12 Sample Paper for 2020 Boards

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

## Evaluate β« |x 2 - 2x| Β dx from 1 to 3

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Note : - This is similar to Example 30 of NCERT β Chapter 7 Class 12

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### Transcript

Question 30 Evaluate β« 3 1 |π₯^2β2π₯| dx |π₯^2β2π₯|=|π₯(π₯β2)| =|π₯| |π₯β2| Thus, π₯=0, π₯=2 Since our integration is from 1 to 3, we ignore x = 0 β΄ |π₯^2β2π₯|= {(π₯Γβ(π₯β2) ππ 1β€π₯<2π₯Γ(π₯β2) ππ 2β€π₯<3)β€ |π₯^2β2π₯|= {(β(π₯^2β2π₯) ππ 1β€π₯<2(π₯^2β2π₯) ππ 2β€π₯<3)β€ Now, β«_1^3 |π₯^2β2π₯| dx = ββ«_1^2β(π₯^2β2π₯) ππ₯+β«_2^3β(π₯^2β2π₯) ππ₯ = ββ«_1^2βπ₯^2 ππ₯+β«_1^2β2π₯ ππ₯+β«_2^3βπ₯^2 ππ₯ββ«_2^3β2π₯ ππ₯ = ββ«_1^2βπ₯^2 ππ₯+β«_2^3βπ₯^2 ππ₯+β«_1^2β2π₯ ππ₯ββ«_2^3β2π₯ ππ₯ = β[π₯^3/3]_1^2+[π₯^3/3]_2^3+[π₯^2 ]_1^2β[π₯^2 ]_2^3 = β[2^3/3β1^3/3]+[3^3/3β2^3/3]+[2^2β1^2 ]β[3^2β2^2 ] = β[8/3β1/3]+[27/3β8/3]+[4β1]β[9β4] = β[7/3]+[19/3]+[3]β[5] = 12/3β2 = 4β2 = 2