Chapter 13.6, Problem 1CP

(a)

To determine

Whether the provided statement “In evaluating ${\displaystyle \int udv}$ parts, the parts $u$ and $dv$ are selected and the parts $du$ and $v$ are calculated”.

(b)

To determine

Whether the provided statement “In evaluating ${\displaystyle \int udv}$ by parts, the differential (often $dx$) is always chosen as a part of $dv$”.

(c)

To determine

Whether the provided statement “In evaluating ${\displaystyle \int udv}$ by parts, the parts $du$ and $v$ are found from $u$ and $dv$ as $du=udx$ and $v={\displaystyle \int dv}$.”

(d)

To determine

Whether the provided statement “For ${\displaystyle \int \frac{3x}{e^{2x}}}dx$, the parts chosen can be $u=3x$ and $dv=e^{2x}dx$.”