Answer to Question #223877 in Chemical Engineering for Lokika

Question #223877

Evaluate ∫y=0^{1}∫x=y^{2√2-y^{2}}y/2√x^{2}+y^{2}dxdy ,by clange the order of integration.


1
Expert's answer
2021-08-30T01:54:13-0400

"\u222b_{y=0}^{1}\u222b_{x=y}^{2\\sqrt{2-y^{2}}} \\frac{y}{2}\\sqrt{x^{2}+y^{2}}dxdy\\\\\n\u222b_{x=0}^{1}\u222b_{y=x}^{\\sqrt{2-\\frac{x^2}{4}}} \\frac{y}{2}\\sqrt{x^{2}+y^{2}}dydx\\\\\n=\\int _0^1\\left(\\frac{\\left(3x^2+8\\right)^{\\frac{3}{2}}}{48}-\\frac{\\sqrt{2}x^3}{3}\\right)dx\\\\\n=\\frac{-48\\sqrt{3}\\ln \\left(2\\right)+32\\sqrt{3}\\ln \\left(\\sqrt{3}+\\sqrt{11}\\right)+23\\sqrt{11}}{192}-\\frac{1}{6\\sqrt{2}}\\\\\n=0.44671"


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