Find the volume of the region bounded above by the surface z equals 3 cosine x sine yz=3cosxsiny and below by the rectangle r: 0 less than or equals x less than or equals startfraction pi over 2 endfraction comma 0 less than or equals y less than or equals startfraction pi over 3 endfractionr: 0≤x≤ π 2, 0≤y≤ π 3.

answer: 0.26

i used the calculator on google

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²