Answer to Question #189384 in Calculus for Sarita bartwal

Question #189384

The function,f is defined by F(x,y)=x^2+xy+y^2 is integrable over [2,1]×[1,2]. True or false with full explanation


1
Expert's answer
2021-05-07T13:41:02-0400

We have given the function,

"F(x,y)=x^2+xy+y^2" over [2,1]×[1,2]

x varies from 2 to 1.

y varies from 1 to 2.

Integrating the given function,

"\\int_{1}^{2} \\int_{2}^{1} (x^2+xy+y^2)dxdy\\\\"


"\\int_{1}^{2}[\\dfrac{x^3}{3}+\\dfrac{x^2y}{2}+xy^2]_{2}^{1}dy"


"= \\int_{1}^{2}[-\\dfrac{7}{3}+\\dfrac{5y}{2}-y^2]dy"


"= [-\\dfrac{7y}{3}+\\dfrac{5y^2}{4}- \\dfrac{y^3}{3}]_{1}^{2}"


"= -\\dfrac{87}{12}"


Hence, the given function is Integrable over [2,1]×[1,2].


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS