Math Help Forum: 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

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

what else do you think could be?

Originally Posted by skeeter

what else do you think could be?

Is it wrong to write ?
Or should I write ? Or it's exactly the same thanks to Fubini?

Originally Posted by arbolis

Is it wrong to write ?
Or should I write ? 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.

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
is maybe good.