Ex 8.1, 13 - Chapter 8 Class 12 Application of Integrals

Transcript

Ex 8.1, 13 Area of the region bounded by the curve 𝑦2=4𝑥, 𝑦-axis and the line 𝑦 = 3 is (A) 2 (B) 9/4 (C) 9/3 (D) 9/3 Given curve 𝑦^2=4𝑥 We have to find area between y-axis and line y = 3 ∴ We have to find area of AOB Area of AOB = ∫1_0^3▒〖𝑥 𝑑𝑦〗 We know that y2 = 4x x = 𝑦^2/4 Now, Area of AOB = ∫1_0^3▒〖𝑥 𝑑𝑦〗 = ∫1_0^3▒〖𝑦^2/4 𝑑𝑦〗 = 1/4 ∫1_0^3▒〖𝑦^2 𝑑𝑦〗 = 1/4 [𝑦^3/3]_0^3 = 1/4 [(3^3 − 0^3)/3] = 1/4 [27/3] = 𝟗/𝟒 Hence, option (B) is correct