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Question 1 - Area between curve and line - Chapter 8 Class 12 Application of Integrals
Last updated at Dec. 16, 2024 by Teachoo
Area between curve and line
Chapter 8 Class 12 Application of Integrals
Concept wise
- Area under curve
- Area bounded by curve and horizontal or vertical line
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Area between curve and line
- Area between curve and curve
Transcript
Question 1 Find the area between the curves 𝑦 = 𝑥 and 𝑦 = 𝑥2 Step 1: Drawing figure Parabola is y = x2 Also, 𝑦=𝑥 passes through (0, 0) & (1, 1) Point (1, 1) lies in parabola y2 = x Hence, intersecting point A = (1, 1) Area required Area required = Area OAD – Area OBAD Area OAD Area OAD = 01𝑦 𝑑𝑥 y → Equation of line y = x Therefore, Area OAD = 01𝑥 𝑑𝑥 = 01𝑥 𝑑𝑥 = 𝑥2201 = 12 12− 02 = 12 Area OBAD Area OBAD = 01𝑦 𝑑𝑥 y → Equation of parabola y = x2 Therefore, Area OBAD = 01 𝑥2 𝑑𝑥 = 𝑥3301 = 13 13− 03 = 13 Area required = Area OAD – Area OBAD = 12 – 13 = 16
