Area Between Curve and y-axis (Leaving Cert Mathematics): Flashcards

$\int_{x_1}^{x_2} y \, dx$

$\int_{y_1}^{y_2} x \, dy$

$y=4$ when $x=2$ in $y=x^2$.

$\int_4^{16} y^{\frac{1}{2}} \, dy$

Expand, integrate each term, and add constant of integration.

Integrate the top curve minus the bottom curve.

Integrate $6x^{3/2}$ from valid limits to find area.

Integrate $\int_1^2 \frac{8}{x^2}-2 \, dx$.

Total area = $\frac{12}{5} + 2 = \frac{22}{5}$.

It links differentiation and integration through antiderivatives.