Week 1: Integration

Guidelines for the quiz 1 (16/17 Sept)

1. Integration by parts: sometimes useful in order to get rid of x, as in

∫xf(x)dx = xF(x)- ∫F(x)dx, where F(x) is an antiderivative of f(x).

Typical example: ∫x sinx dx=-x cos x+∫cos x dx=-x cos(x) + sin(x) +C

2. The trigonometric identities that we used fall into two categories:

i) involving sin and cos which are useful when dealing with (even ) powers of sin and cos

ii) involving tan and sec, which are the main tool when dealing with indefinite integrals of powers ∫tan^nxdx, ∫sec^nxdx.