# 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 $$-sqrt{1-x^2}-e^xle ylesqrt{1-x^2}-e^x.$$

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

## Related Questions

### What is the solution of this summation?

4  Asked on February 12, 2021 by arko-chowdhury

### Number of fixed points of a random permutation

1  Asked on February 12, 2021 by aliba

### Find $a$, $b$ such that $x^2 – x -1$ is a factor of $ax^9 + bx^8 + 1$

6  Asked on February 12, 2021 by aniruddha-deb

### “Standard theorem on differential equations” that implies a function is analytic

0  Asked on February 12, 2021 by stannisba

### Identity up to isomorphism treated as identity in proof

1  Asked on February 12, 2021 by roland-salz

### Burnside’s Lemma bracelet with beads in 2 colours (uneven cardinality)

1  Asked on February 12, 2021 by patrycja

### Prove $2^{lceil lg (n-1) rceil} ge n-1$

1  Asked on February 12, 2021 by hiep

### Identify boolean function that satisfies some constrains

1  Asked on February 11, 2021

### How to show that the curve $ay^2=x(x-a)(x-b)$ has two and only two points of inflexion?

1  Asked on February 11, 2021 by theunixdisaster

### volume under a 3-d curve

0  Asked on February 11, 2021

### Groups of $3$ out of $23$ s.t. all students cooperate exactly once

2  Asked on February 11, 2021 by nikolaos-skout

### (Manifolds) Prove the following is a sufficient condition for a function to be a morphism between manifolds

0  Asked on February 11, 2021 by itamar-e-aharoni

### existence of countably additive measure for Borel subsets of $[0,1]$

1  Asked on February 11, 2021

### Are the two spans equal?

3  Asked on February 11, 2021 by martyna

### Simplifying iterated sums where the upper bound is the next index

1  Asked on February 11, 2021 by user196574

### Mathematical Writing: Can objects in a definition be assigned any name, even though this name is used elsewhere in the text?

1  Asked on February 11, 2021 by clapham

### $T:P_nlongrightarrow P_n : Tp(t)=frac{d}{dt}p(t)text{ Find the norm of the operator}$

1  Asked on February 11, 2021

### Method to solve an equation

1  Asked on February 10, 2021 by khosrotash

### Prove that $sum_{n=1}^infty frac{x^{2n}}{(n+x)^2}$ converges uniformly on $S=[0,1]$

0  Asked on February 10, 2021 by naturalmathlover

### Find moment generating function for $sqrt{n}(overline{X}-1)$

0  Asked on February 10, 2021 by diego-andres-gomez-polo