# Ex 8.1, 2 - Chapter 8 Class 12 Application of Integrals

Last updated at Nov. 15, 2019 by Teachoo

Last updated at Nov. 15, 2019 by Teachoo

Transcript

Ex 8.1, 2 Find the area of the region bounded by y2 = 9𝑥, 𝑥 = 2, 𝑥 = 4 and the 𝑥-axis in the first quadrant. Let AB represent line 𝑥=2 CD represent line 𝑥=4 and CBOAD represent the curve 𝑦2=9𝑥 We have to find area of BCFE Area of BCFE = 24𝑦 .𝑑𝑥 So, we need to calculate 24𝑦 .𝑑𝑥 We know that 𝑦2=9𝑥 Taking square root on both side ∴ 𝑦=± 9𝑥 ∴ 𝑦=±3 𝑥 Since BCFE is in 1st Quadrant ∴ 𝑦=3 𝑥 Area of BCFE = 24𝑦 .𝑑𝑥 = 3 24 𝑥𝑑𝑥 = 3 24 𝑥 12𝑑𝑥 = 3 𝑥 12 + 1 12 + 1 24 = 3 𝑥 32 3224 = 3 × 23 𝑥 3224 = 2 4 32 − 2 32 = 2 4 123− 2 123 = 2 23− 23 = 2 8 −2 2 = 16 – 4 2 Thus , Area = 16 – 4 𝟐 square units

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.