Evaluate the double integral by first identifying it as the volume of a solid. 3 da, r = {(x, y) | −1 ≤ x ≤ 1, 3 ≤ y ≤ 8} r

a

step-by-step explanation:

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

answer4 to the second power is 16

and 4 to the third power is 64,