When solving problems on multiple integration, why are the limits of integration functions of y, if integrating with respect to x. Please can you explain it graphically?
Edit:
In single variable integration, the limits of integration a and b are typically along the axis of the variable of integration which is x in this case $$\int_a^b f(x) \,dx$$
But in multiple integration, we have $$\int_{h_1(y)}^{h_2(y)} f_x(x, y) \,dx= f(x, y) \bigg\rvert_{h_1(y)}^{h_2(y)} = f(h_2(y), y) - f(h_1(y), y)$$ with respect to x, and
$$\int_{g_1(x)}^{g_2(x)} f_y(x, y) \,dy= f(x, y) \bigg\rvert_{g_1(x)}^{g_2(x)} = f(x, g_2(x)) - f(x, g_1(x))$$ with respect to y
- from Larson Edwards Calculus, section 14.1
So when integrating with respect to x, why were the limits of integration expressed as functions of y?