Evaluating Definite Integrals by Finding Antiderivatives Questions (4)

Evaluate $$\int_{1}^{2} 2x dx$$

If $f(x) = \begin{cases} x, & x < 1 \\ \sin x, & x \geq 1 \end{cases}$, find $$\int_{0}^{\pi} f(x) dx$$

Evaluate $$\int_{0}^{1} \frac{\sin^{-1} x}{\sqrt{1-x^2}} dx$$

Evaluate $$\int_{0}^{\ln 2} \frac{e^x}{1+e^x} dx$$