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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 You are here
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
Example 14 Important Deleted for CBSE Board 2023 Exams
Area between curve and line
Last updated at Dec. 8, 2016 by Teachoo
Misc 10 Find the area of the region enclosed by the parabola 𝑥2=𝑦, the line 𝑦=𝑥+2 and the 𝑥−axis Step 1: Draw the Figure Parabola is 𝑥2=𝑦 Also, 𝑦=𝑥+2 is a straight line Step 2: Finding point of intersection A & B Equation of line is 𝑦=𝑥+2 Putting value of y in equation of parabola 𝑥2=𝑦 𝑥2=𝑥+2 𝑥2−𝑥−2=0 𝑥2−2𝑥+𝑥−2=0 𝑥(x−2) +1(𝑥−2)=0 (𝑥+1)(𝑥−2)=0 So, x = –1, x = 2 Required Area Area required = Area ADOEB – Area ADOEBC Area ADOEB Area ADOEB = −12𝑦 𝑑𝑥 y → Equation of line y = x + 2 Therefore, Area ADOEB = −12 𝑥+2 𝑑𝑥 = 𝑥22+2𝑥−12 = 222+2 2− −122+2 −1 = 2+ 4 – 12 + 2 = 152 Area ADOEBC Area ADOEBC = −12𝑦 𝑑𝑥 y → Equation of parabola 𝑥2=𝑦 𝑦= 𝑥2 Therefore, Area ADOEBC = −12 𝑥2 𝑑𝑥 = 𝑥33−12 = 13 23− −13 = 93 = 3 Area required = Area ADOEB – Area ADOEBC = 152 – 3 = 92