Question

I have a conceptual question about integration

Answer 1

when you use the fundamental theorem of calculus to find the value between an upper and lower bound, is that essentially calculating the area under the curve?

Answer 2

yes

Answer 3

then why do we not give the answer as a square? wouldnt that be more appropriate for "area"

Answer 4

no we can't since in squares we have all sides equal

Answer 5

well what i meant is if you calculate an area it is two dimensional, so instead of the answer being something like 16 shouldnt it be 16^2? this would signify that the area is two dimensional. concrete is calculated as a three dimensional object and is therefore given in cubic yards or yards^3. that doesn't mean that the concrete is a perfect square on all three sides

Answer 6

You should remember that the main purpose of integration is that it is used where the dimensions are not uniform