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Area between curve and curve
Misc 13
Ex 8.2, 4 Important Deleted for CBSE Board 2023 Exams
Ex 8.2, 5 Important Deleted for CBSE Board 2023 Exams
Misc 14 Important
Misc 4 Important
Misc 11 Important
Ex 8.2,1 Important Deleted for CBSE Board 2023 Exams
Misc 15 Deleted for CBSE Board 2023 Exams
Example 7 Important Deleted for CBSE Board 2023 Exams
Misc 18 (MCQ) Deleted for CBSE Board 2023 Exams
Example 15 Important You are here
Ex 8.2, 2 Deleted for CBSE Board 2023 Exams
Example 10 Important Deleted for CBSE Board 2023 Exams
Example 6 Important Deleted for CBSE Board 2023 Exams
Misc 19 (MCQ) Important Deleted for CBSE Board 2023 Exams
Area between curve and curve
Last updated at Dec. 12, 2019 by Teachoo
Example 15 Find the area of the region {(π₯, π¦) : 0 β€ π¦ β€ π₯2 + 1, 0 β€ π¦ β€ π₯ + 1, 0 β€ π₯ β€ 2} Here, πβ€πβ€π^π+π π¦β₯0 So it is above π₯βππ₯ππ π¦=π₯^2+1 i.e. π₯^2=π¦β1 So, it is a parabola πβ€πβ€π+π π¦β₯0 So it is above π₯βππ₯ππ π¦=π₯+1 It is a straight line Also πβ€πβ€π Since π¦β₯0 & 0β€π₯β€2 We work in First quadrant with 0β€π₯β€2 So, our figure is Finding point of intersection P & Q Here, P and Q are intersection of parabola and line Solving π¦=π₯^2+1 & π¦=π₯+1 π₯^2+1=π₯+1 π₯^2βπ₯+1β1=0 π₯^2βπ₯+0=0 π₯(π₯β1)=0 So, π₯=0 , π₯=1 For π = 0 π¦=π₯+1=0+1=1 So, P(0 , 1) For π = 1 π¦=π₯+1=1+1=2 So, Q(1 , 2) Finding area Area required = Area OPQRST Area OPQRST = Area OPQT + Area QRST Area OPQT Area OPQT =β«_0^1βγπ¦ ππ₯γ π¦β equation of Parabola PQ π¦=π₯^2+1 β΄ Area OPQT =β«_0^1β(π₯^2+1) =[π₯^3/3+π₯]_0^1 =[1^3/3+1]β[0^3/3+0] =1/3+1 =4/3 Area QRST Area QRST=β«_1^2βγπ¦ ππ₯γ Here, π¦β equation of line QP π¦=π₯ + 1 β΄ Area QRST=β«_1^2β(π₯+1) ππ₯ =[π₯^2/2+π₯]_1^2 =(2^2/2+2)β(1^2/2+1) =2+2β(1/2+1) =4β3/2 =5/2 Thus, Area Required = Area OPQT + Area QPST = 4/3+5/2 = (8 + 15)/6 = ππ/π square units