Let \( {\bf F}=\langle y^{3}-1, 3xy^{2}+\frac{1}{y} \rangle\…
Let \( {\bf F}=\langle y^{3}-1, 3xy^{2}+\frac{1}{y} \rangle\). Find \( \int_{C} {\bf F} \cdot {\bf dr}\) if \(C\) is the curve defined by \({\bf r}(t)=\langle \sin^{3}(t), e^{t} \rangle\) where \(0 \leq t \leq \pi\). Hint: The curve is NOT a closed path. Use FTLI.
Read Details