# Math Help - mass

1. ## mass

The question:
A cardboard figure has the shape shown below. The region is bounded on the left by the line x = a, on the right by the line x = b, above by f(x), and below by g(x). The density p(x) in gm/ cm2 varies only with x.

Find the integral needed for the total mass of the figure. Give your answer using the form below.

I know that A =a and B=b as far as the limit of integration and that the area is (f(x)-g(x)) dx so mass is
(f(x)-g(x)) dx* p(x) but im not sure how to expresses it as H(x), and anyone please help. Thank you

2. Originally Posted by acosta0809
The question:
A cardboard figure has the shape shown below. The region is bounded on the left by the line x = a, on the right by the line x = b, above by f(x), and below by g(x). The density p(x) in gm/ cm2 varies only with x.

Find the integral needed for the total mass of the figure. Give your answer using the form below.

I know that A =a and B=b as far as the limit of integration and that the area is (f(x)-g(x)) dx so mass is
(f(x)-g(x)) dx* p(x) but im not sure how to expresses it as H(x), and anyone please help. Thank you
$H(x) = \rho(x)[f(x)-g(x)]dx$

what else do you think $H(x)$ could be?

3. Originally Posted by skeeter
$H(x) = \rho(x)[f(x)-g(x)]dx$

what else do you think $H(x)$ could be?
Is it wrong to write $\int_a^b \rho(x)[f(x)-g(x)]dx = \int_{g(x)}^{f(x)} \int_a^b \rho (x) dxdy$?
Or should I write $\int_a^b \rho(x)[f(x)-g(x)]dx =\int_a^b \int_{g(x)}^{f(x)} \rho (x) dydx$? Or it's exactly the same thanks to Fubini?

4. Originally Posted by arbolis
Is it wrong to write $\int_a^b \rho(x)[f(x)-g(x)]dx = \int_{g(x)}^{f(x)} \int_a^b \rho (x) dxdy$?
Or should I write $\int_a^b \rho(x)[f(x)-g(x)]dx =\int_a^b \int_{g(x)}^{f(x)} \rho (x) dydx$? Or it's exactly the same thanks to Fubini?
Been awhile since I've done double integrals, but if I remember correctly, the outside integral must have constant limits of integration.

5. Originally Posted by skeeter
Been awhile since I've done double integrals, but if I remember correctly, the outside integral must have constant limits of integration.
Ah you're right. So $\int_a^b \int_{g(x)}^{f(x)} \rho (x) dydx$
is maybe good.