Finding Areas by Integration (HSC SSCE Mathematics Advanced): Flashcards

Area vs definite integral: key difference

Area always positive; integral can be positive or negative

Integral sign when curve above $x$-axis

Positive

Integral sign when curve below $x$-axis

Negative

Finding area when curve crosses $x$-axis

Split at intercepts, add absolute values of separate integrals

Odd function definition: $f(-x) = ?$

$-f(x)$

Odd function symmetry type

180° rotational symmetry about origin

Using symmetry for odd functions to find area

Calculate one region and double it

What does $\int_a^b x \, dy$ represent?

Signed area between curve and $y$-axis

Three steps for finding areas by integration

1. Sketch 2. Integrate 3. Conclude with square units

When integral is negative, how to get area

Take absolute value