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Misc 3 - Chapter 8 Class 12 Application of Integrals
Last updated at April 16, 2024 by Teachoo
Area bounded by curve and horizontal or vertical line
Chapter 8 Class 12 Application of Integrals
Concept wise
- Area under curve
-
Area bounded by curve and horizontal or vertical line
- Area between curve and line
- Area between curve and curve
Transcript
Misc 3 Find the area bounded by the curve π¦=sinβ‘π₯ between π₯=0 and π₯=2π Area Required = Area OAB + Area BCD Area OAB = β«_0^πβγπ¦ ππ₯γ π¦βsinβ‘π₯ = β«_π^π βγπ¬π’π§β‘π π πγ = [βcosβ‘π₯ ]_β( @0)^π =β [cosβ‘πβcosβ‘0 ] =β[β1β1] =β[β2] = 2 Area BCD = β«_π^2πβγπ¦ ππ₯γ = β«_π ^ππ βγπππβ‘π π πγ = [βcosβ‘π₯ ]_β( @ @π)^2π =β [cosβ‘2πβcosβ‘π ] =β[1β(β1)] = β 2 Since area cannot be negative, Area BCD = 2 Hence, Area Required = Area OAB + Area BCD = 2+2 = π square units
