use the given transformation to evaluate the integral. 2y2 da, r where r is the region bounded by the curves xy = 2, xy = 4, xy2 = 2 and xy2 = 4; u = xy, v = xy2

x + 4/7

step-by-step explanation:

use cymath

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: rolling a number cube and flipping a coin.

step-by-step explanation: