Evaluate the integral below given R. (Hint: what is the upper boundary of x?)

Question

Evaluate the integral below given R. (Hint: what is the upper boundary of x?)

 

 

∫∫1_R^  xy da

R bounded by
x=0y=0y=9−x^2

 

 

 

Answer 1

Greetings! Lets solve this shall we ?

Let the double integral be equal to the following to be integrated around the given boundaries such that,

y = 9 - x² , where at y = 0, x = ±3 and the upper boundary is x = +3. Therefore,

∫₀⁹ ∫_-3³ xy dxdy

= ∫₀⁹ y(x²/2)_-3³ dy = ∫₀⁹ 0 dy

= C]₀⁹ = 9

I hope this helped!