AnswerBun.com

Area of $A:= lbrace (x,y) in mathbb{R}^2 : x^2+(e^x +y)^2leq1 rbrace$

Mathematics Asked by marvel on December 18, 2020

I am having trouble calculating the area of $$A:= {lbrace(x,y) in mathbb{R}^2 : x^2+(e^x +y)^2leq1 rbrace}.$$ I hope someone can help me.

I have tried using Fubini with the following boundaries for $x$ and $y$:

$$-1le xle1 ,$$ and $$-sqrt{1-x^2}-e^xle ylesqrt{1-x^2}-e^x.$$

One Answer

Use Cavalieri's principle. The area is $int_{-1}^12sqrt{1-x^2}dx$, just like the circle we'd get without the $e^x$ term, i.e. $pi$.

Correct answer by J.G. on December 18, 2020

Add your own answers!

Related Questions

What is the solution of this summation?

4  Asked on February 12, 2021 by arko-chowdhury

     

volume under a 3-d curve

0  Asked on February 11, 2021

     

Are the two spans equal?

3  Asked on February 11, 2021 by martyna

   

Ask a Question

Get help from others!

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP