Q1: Let $\gamma: [0,1] \rightarrow \mathbb{C}$ be a continuous map. Which statement is not correct?

A1: $ \int_0^1 \gamma(t) dt $ is well-defined.

A2: $ \int_0^1 \gamma(t) dt $ is a complex number.

A3: $ \int_0^1 \gamma(t) dt $ is an antiderivative of $\gamma$.

A4: $ \int_0^1 \gamma(t) dt $ has a real and an imaginary part.

Q2: Let $\gamma: [0,1] \rightarrow \mathbb{C}$ be given by $\gamma(t) = 2t + i 4 t^3$. What is $ \int_0^1 \gamma(t) dt $?

A1: $1$

A2: $1 + i$

A3: $2$

A4: $2 + 4 i$

Q3: Which number is larger than $$ \left| \int_0^1 \exp(\pi i t) dt \right| $$

A1: $1$

A2: $\frac{1}{2}$

A3: $\frac{1}{\pi}$

A4: $0$