(Solved): (a) \( \int_{0}^{3} \frac{1}{3} x d x+\int_{3}^{4}(4-x) d x \) gives the area of a region using \( ...

(a) \( \int_{0}^{3} \frac{1}{3} x d x+\int_{3}^{4}(4-x) d x \) gives the area of a region using \( d x \) integrals. Set up a \( d y \) integral that gives the area of the same region. (b) The following integral gives the area of a region using a \( d y \) integral: \[ \int_{0}^{2}[(4-2 y)-(y-2)] d y \] Set up an expression using one or more \( d x \) integrals that gives the area of the same region.