Mathematics
Session Definite Integrals - 3
Session Objectives Definite Integral as the Limit of a Sum Areas of Bounded Regions Class Exercise
Definite Integral as the Limit of a Sum OR
Example - 1
Solution Cont.
Example - 2
Solution Cont.
Example - 3
Solution Cont.
Example - 4
Solution Cont.
Example - 5
Solution Cont.
Areas of Bounded Regions 1. Let f(x) be a continuous function defined on the interval [a, b]. Then, the area bounded by the curve y = f(x), x-axis and the ordinates x = a, x = b is The area bounded by the curve x = f(y), y-axis and the abscissae y = c, y = d is
Areas of Bounded Regions Cont.
Example - 6
Solution Cont.
Example - 7
Solution Cont.
Solution Cont.
Example - 8 Solution: The given curves are (i) and (ii) intersect at (1, 0) and (0, 1).
Solution Cont.
Example - 9
Solution Cont.
Example - 10 Solution: The given curves are
Solution Cont.
Solution Cont.
Solution Cont.
Example - 11
Solution Cont. x' x y y' O (1, 0) x2 + y2 = 1 (x - 1)2 + y2 = 1
Solution Cont.
Solution Cont.
Thank you