Today we need to work on integration, in particular integration by parts.
- Compute $\int e^{2x}dx.$
- Compute $\int xe^{2x}dx.$
- Compute $\int x^2e^{2x}dx.$
- Find $\frac{dy}{dx}$ if $x^2+2xy^2+3y=4$.
- If $A=x^2$, find $dA$ in terms of $x$ and $dx$.
- If $A=xy$, find $dA$ in terms of $x, y, dx, dy$.
- Compute $d(uv)$ in terms of $u,v, du,dv$. Then solve for $vdu$ and integrate to explain where integration by parts comes from.
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