Mathematics Quick Revision

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Class 12 Chapter 7 - Application of Integrals

Quick Revision

Area under Simple Curves

● Total area `A` of the region between x-axis, ordinates `x = a, x = b` and the curve `y = f (x)` as the result of adding up the elementary areas of thin strips across the region PQRSP. Symbolically, we express

● Here, we consider vertical strips as shown in the Fig

`color{blue} {A = int_a^b d A = int_a^b ydx = int_a^b f(x) dx}`

Area between Two Curves

`A = ["area bounded by" y = f (x), "x-axis and the lines"\ \ x = a, x = b]`
`– ["area bounded by" y = g (x), "x-axis and the lines" \ \ x = a, x = b]`

`color {red} {= int_a^b f(x) dx - int_a^b g(x) dx = int_a^b [ f(x) - g(x) ] dx}` , where `f(x) >= g(x) ` in `[ a,b]`