Question

Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?

Options

• \[A=4\int_0^a y\,dx\]

• \[A=\int_a^b y\,dx=\int_a^b f(x)\,dx\]

• \[A=\int_c^d x\,dy=\int_c^d g(y)\,dy\]

• \[A=\left|\int_a^b f(x)\,dx\right|\]

Answer 1

The elementary area is \[x\cdot dy\] for a horizontal strip. Adding these strips from \[y=c\] to \[y=d\] gives \[A=\int_c^d x\,dy\].