Question

Find a formula for the area of the ellipse 2) -1 by slicing vertically. Sketch the ellipse, + b2 a clearly showing a representative vertical slice. Show your Riemann sum and definite integral Recall that this is an ellipse centered at the origin with major axis length of 2a and minor axis length of 2b Note: If a b, what do you notice about your formula?

Answer 1

Soluton Areaof the ellupse a2 minor axts 2b mazor ayo/s 2a, Rteman n Sum n A0o ao) dx a,0 Deftniitgat flx) dax a y dx 4 4- 7 a Coso, yzbsire Here X dacs) rea (bsine) 4 in2o ty2 -4ab -Cosds 4ab 2 =ab e-in2 2 TTab (n magn'tude) area Then fEtpsc dAn ...