CBSE Class 12 Sample Paper for 2026 Boards
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CBSE Class 12 Sample Paper for 2026 Boards
Last updated at September 2, 2025 by Teachoo
This question is similar to Chapter 8 Class 12 Application of Integrals - Miscellaneous
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Transcript
Question 28 (A) Sketch the graph π¦=|π₯+1|. Evaluate β«_(β4)^2β|π₯+1|ππ₯. What does the value of this integral represent on the graph? |π₯+1|= {β( (π₯+1) ππ π₯+1β₯0@β(π₯+1) ππ π₯+1<0)β€ = {β((π₯+1) ππ π₯β₯β1@β(π₯+1) ππ π₯<β1)β€ Letβs Draw the graph y = |π+π| We need to find β«_(β4)^2β|π₯+1|ππ₯ This is area of curve |π+π| and x-axis between x = β4 and x = 2 Letβs find it Now, β«_(βπ)^πβγβπ+πβ π πγ =β«_(β4)^(β1)βγβπ₯+1β ππ₯γ+β«_(β1)^2βγβπ₯+1β ππ₯γ =β«_(βπ)^(βπ)βγβ(π+π) π π +β«_(βπ)^πβγ(π+π) π πγγ =[βπ₯^2/2βπ₯]_(β4)^(β1) +[π₯^2/2+π₯]_(β1)^( 2) =[(β(β1)^2)/( 2)β (β1)]β[(β(β4)^2)/( 2)β(β4)] +[2^2/2+ 2]β[(β1)^2/2+ (β1)] =[(β1)/( 2)+1]β[(β16)/( 2)+4]+[2+2]β[1/2β1] =[1/( 2)]β[β8+4]+[4]β[(β1)/2] =[1/( 2)]β[β4]+[4]β[(β1)/2] =1/2+4+4+1/2 =1/2+1/2+8 =1+8 =π
