Integration

Integration problems on the test are typically basic definite integrals of polynomials. Integration is the reverse of differentiation (the anti-derivative). For a term $ax^n$, its integral is $\frac{a}{n+1}x^{n+1}$.

To evaluate a definite integral $\int_a^b f(x)dx$, you find the anti-derivative $F(x)$ and then compute $F(b) - F(a)$.

A key shortcut: The integral of an odd function over a symmetric interval $[-a, a]$ is always zero. For example, $\int_{-\pi/4}^{\pi/4} \sin(x) dx = 0$ because sin(x) is an odd function.