1. Calculate area of x-y

Could someone please check my work?

$\int \int_D (x-y) dA$

where D is bounded by $y=\sqrt{x}$ and $y=x^2$

I evaluated the double integral as
$\int_0^1 \int_{x^2}^{\sqrt{x}} (x-y) dy dx$

Solving the definite integral, the answer got was $\frac{1}{15}$.

Is this correct?

2. Re: Calculate area of x-y

Originally Posted by tammyl
Could someone please check my work?

$\int \int_D (x-y) dA$

where D is bounded by $y=\sqrt{x}$ and $y=x^2$

I evaluated the double integral as
$\int_0^1 \int_{x^2}^{\sqrt{x}} (x-y) dy dx$

Solving the definite integral, the answer got was $\frac{1}{15}$.

Is this correct?

-Dan

3. Re: Calculate area of x-y

Scary that I manage the calculus and mess up the adding of fractions.

Thank you greatly for your help!!!

4. Re: Calculate area of x-y

Originally Posted by tammyl
Scary that I manage the calculus and mess up the adding of fractions.

Thank you greatly for your help!!!
It's a more common problem than you might think.

-Dan

5. Re: Calculate area of x-y

Originally Posted by tammyl
Scary that I manage the calculus and mess up the adding of fractions.
Yes, it means you are destined to be a mathematician!

Be afraid. Be very afraid!

Thank you greatly for your help!!!