Tutorial Week 8

Improper Integrals

Q1: Evaluate \(\int_1^\infty \frac{e^x}{e^{2x} + 3e^x + 2} \; dx\).

Show Solution

Q2: Evaluate \(\int_{-1}^1 \frac{1}{x^{\frac{2}{3}}} \; dx\).

Show Solution

Q3: For which values of \(a\) (if \(a \neq -1\)) does \(\int_1^\infty x^a \; dx\) converge or diverge?

Show Solution

Comparison Test

Q4: Does \(\int_{-\infty}^{-1} \frac{\sin\left(x\right)^{2}\cos\left(x\right)^{2}}{x^{2}} \; dx\) converge or diverge?

Show Solution