Question 1001a

Definite Integrals: Areas and Volumes

Area Under Parametric Curves

Question

The curve

{C}

has parametric equations

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

for

{t \geq -1.}

Find the area bounded by ${C,}$ the ${x\textrm{-axis}}$ and the lines ${x=- 2}$ and ${x=6.}$ Leave your answers correct to 2 decimal places.