Slide13.JPG

Slide14.JPG
Slide15.JPG

Go Ad-free

Transcript

Example 4 Find the area bounded by the curve 𝑦=cos⁑π‘₯ between π‘₯=0 and π‘₯=2πœ‹Area OAB = ∫_0^(πœ‹/( 2))▒〖𝑦 𝑑π‘₯γ€— 𝑦→cos⁑π‘₯ = ∫_𝟎^(𝝅/( 𝟐))▒〖𝒄𝒐𝒔⁑𝒙 𝒅𝒙〗 = [sin⁑π‘₯ ]_0^(πœ‹/2) =sinβ‘γ€–πœ‹/2βˆ’sin⁑0 γ€— =1βˆ’0 =𝟏 Area BCD = ∫_(πœ‹/( 2))^(3πœ‹/( 2))▒〖𝑦 𝑑π‘₯γ€— = ∫_(𝝅/( 𝟐))^(πŸ‘π…/( 𝟐))▒〖𝒄𝒐𝒔⁑𝒙 𝒅𝒙〗 = [sin⁑π‘₯ ]_(πœ‹/( 2))^(3πœ‹/( 2)) = sin 3πœ‹/( 2)βˆ’sinβ‘γ€–πœ‹/( 2)γ€— = – 1 – 1 = –2 Since area cannot be negative Area BCD = 2 Area DEF = ∫_(3πœ‹/( 2))^2πœ‹β–’γ€–π‘¦ 𝑑π‘₯γ€— = ∫_(πŸ‘π…/( 𝟐))^πŸπ…β–’γ€–π’„π’π’”β‘π’™ 𝒅𝒙〗 = [sin⁑π‘₯ ]_(3πœ‹/( 2))^2πœ‹ =sin⁑2πœ‹ βˆ’sin⁑〖3πœ‹/( 2)γ€— = 0βˆ’(βˆ’1) = 𝟏 Therefore Area Required = Area OAB + Area BCD + Area DEF = 1 + 2 + 1 = 4 square unit

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.