# Calculate area of x-y

• April 30th 2013, 04:53 AM
tammyl
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?
• April 30th 2013, 06:30 AM
topsquark
Re: Calculate area of x-y
Quote:

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
• April 30th 2013, 07:03 AM
tammyl
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!!!
• April 30th 2013, 12:04 PM
topsquark
Re: Calculate area of x-y
Quote:

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. (Beer)

-Dan
• April 30th 2013, 01:15 PM
HallsofIvy
Re: Calculate area of x-y
Quote:

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!

Quote:

Thank you greatly for your help!!!