Question 1001a

Definite Integrals: Areas and Volumes

Area Under Parametric Curves

Question

The curve

{C}

has parametric equations

\begin{align*} x&=t^2 + 4 t - 1, \\ y&=\frac{1}{4} t^3 + t + 5 \end{align*}

for

{t \geq -2.}

Find the area bounded by ${C,}$ the ${x\textrm{-axis}}$ and the lines ${x=- 5}$ and ${x=- 4.}$ Leave your answers correct to 2 decimal places.