Tutorial Week 3

Assignment Review

Q1: Evaluate \(\int \frac{1}{cos(x) + 2}dx\).

Show Solution

* There’s a mistake in the last line; it should be \(\frac{2}{\sqrt{3}}\). The substitution is also wrong since it should be \(w = \frac{1}{\sqrt{3}}tan(\frac{x}{2})\).

Integral Practice

Q2: Evaluate \(\int \frac{1}{1-cos(x)} dx\).

Show Solution

Q3: Evaluate \(\int_{-5}^{5} \frac{\arctan\left(x\right)\sin^2\left(x\right)x^{2}}{1+2x^{2}} dx\).

Show Solution

Q4: Evaluate \(\int arctan(1/x)dx\).

Show Solution