Question 1001a

Definite Integrals: Areas and Volumes

Area Under Parametric Curves

Question

The curve

{C}

has parametric equations

\begin{align*} x&=t^2 - 6 t + 1, \\ y&=\frac{1}{9} t^3 + t + 1 \end{align*}

for

{t \leq 3.}

Find the area bounded by ${C,}$ the ${x\textrm{-axis}}$ and the lines ${x=- 8}$ and ${x=- 7.}$ Leave your answers correct to 2 decimal places.