Answer
a)
$\frac{dy}{dx}=\frac{dy/dt}{dx/dt}$.
b)
$\int_{a}^{b} ydx = \int_{α}^{β} g(t)f'(t)dt$.
Work Step by Step
a)
The slope of a tangent to a parametric curve is defined as $\frac{dy}{dx}$. It can be written as a function of $t$, so $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}$. To find the value of the tangent, we can evaluate the derivatives of the two functions that defined the curve.
b)
To calculate the area under the parametric curve, we can use the integral $\int_{a}^{b} ydx = \int_{α}^{β} g(t)f'(t)dt$.
