Area under Curve

 Calculus was historically developed to find a general method for determining the area of geometrical figures.  When these figures are bounded by curves, their areas cannot be determined by elementary geometry.  Integration can be applied to find such areas accurately.

 Also known as Trapeziod/Trapezium Rule  An approximating technique for calculating area under a curve  Works by approximating the area as a trapezium

Actual Area = units 2.

(2, 4) (1, 1) From diagram, clearly, it is an overestimate. Actual Area = 2.67 units 2.

- Show Geogebra

Dividing the area under the line into 4 strips, We will start to approximate the area by finding the area of the rectangles Width of each rectangle = 0.25

width of each rectangle = 0 Find the height of each rectangle Write down the statement for the area of each rectangle and sum them up

Dividing the area under the line into n strips, width of each rectangle = 0

0 As we increase the no. of rectangles, the white triangles will be filled up by the rectangles and we will get a better approximation of the area.

Similarly, we divide the area under the curve into n strips. width of each rectangle = Find the height of each rectangle Write down the statement for the area of each rectangle and sum them up

Similarly, we divide the area under the curve into n strips. width of each rectangle =

Find the area under the curve between x = 3 and x = 6 Find the area under the curve between x = 3 and x = 6

Adding both sides,