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Area between curve and line
Ex 8.1, 6 Important
Ex 8.2, 6 (MCQ) Deleted for CBSE Board 2023 Exams
Example 8 Important Deleted for CBSE Board 2023 Exams
Misc 8
Misc 9 Important
Ex 8.2 , 7 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 6 Important
Misc 2 Deleted for CBSE Board 2023 Exams
Misc 10
Ex 8.1, 10 Important
Misc 7
Ex 8.1, 9
Misc 12 Important Deleted for CBSE Board 2023 Exams
Ex 8.2, 3 Important Deleted for CBSE Board 2023 Exams You are here
Example 14 Important Deleted for CBSE Board 2023 Exams
Area between curve and line
Last updated at Dec. 12, 2019 by Teachoo
Ex 8.2 , 3 Find the area of the region bounded by the curves 𝑦=𝑥2+2, 𝑦=𝑥, 𝑥=0 and 𝑥=3 Here, 𝑦=𝑥2+2 𝑦−2=𝑥^2 𝑥^2=(𝑦−2) So, it is a parabola And, 𝑥=𝑦 is a line x = 3 is a line x = 0 is the y-axis Finding point of intersection B & C Point B Point B is intersection of x = 3 and parabola Putting 𝑥=3 in 𝑥^2=(𝑦−2) 3^2=(𝑦−2) 9 = 𝑦−2 𝑦=11 Hence, B = (3 , 11) Point C Point C is the intersection of x = 3 and x = y Putting 𝑥=3 in 𝑥=𝑦 3=𝑦 i.e. 𝑦=3 Hence C = (3 , 3) Finding Area Area required = Area ABDO – Area OCD Area ABDO Area ABDO = ∫_0^3▒〖𝑦 𝑑𝑥〗 𝑦→ Equation of parabola AB 𝑦=𝑥^2+2 ∴ Area ABDO = ∫_0^3▒〖𝑦 𝑑𝑥〗 = ∫_0^3▒〖(𝑥^2+2) 𝑑𝑥〗 = [𝑥^3/3+2𝑥]_0^3 = [3^3/3+2 ×3−0^3/3] = 9+6 = 15 Area OCD Area OCD = ∫_0^3▒〖𝑦 𝑑𝑥〗 𝑦→ equation of line 𝑦=𝑥 ∴ Area OCD = ∫_0^3▒〖𝑦 𝑑𝑥〗 = ∫_0^3▒〖𝑥 𝑑𝑥〗 = [𝑥^2/2]_0^3 =[3^2/2−0^2/2] = 9/2 Area required = Area ABDO – Area OCD = 15 – 9/2 = 𝟐𝟏/𝟐 square units