7 2  areas.notebook

7 2  areas.notebook

2 ways...find time t, when v = 0, then double since parabolic and starts at (0, 0)or find s(t) integrating the vel. function, (find c by sub in (0, 0)) then set = 0.

double max ht. or integrate velocity function from t = 0 to t = 5.625

0, since it ends where it started.

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

Find the area of the region enclosed by the parabola y = 4 - x2 and the parabola y = x2 - 4

Find the area of the region enclosed by the parabola y = -3x2 + 5 and the line y = 2x

7 2  areas.notebook

Find the area of the region R in the first quadrant that is bounded above by y = 3√x , below by the x-axis, and the line y = 3x - 6.

Areas, using subregions

think of the width of the rectangles as a change in y (dy) and the length of each rectangle as one x-value (further right) minus corresponding x-value (found to left)

7 2  areas.notebook

7 2  areas.notebook

Find the area of the region between the curve x = y2 - 4y and the line x = y.

sin2x = ½ - ½ cos (2x)cos (2x) = cos2x - sin2x

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook

7 2  areas.notebook