Areas and the Definite Integral (HSC SSCE Mathematics Advanced): Flashcards

Rectangle area = length×breadth; dissection preserves area

$\int$ (elongated S for Sum)

Integrand

Lower and upper limits (or bounds)

$\frac{1}{2}bh$

$\frac{1}{2}(a+b)h$ (average of parallel sides × width)

$\pi r^2$

Area under curve $y=f(x)$ from $x=a$ to $x=b$

$f(x) \delta x$ (height × width)

True integral value lies between lower and upper sums