The wedge in Figure (a) has area

The wedge in Figure (a) has area $\frac{1}{2}{r}^{2}d\theta$. One reason: It is a fraction $d\theta /2\pi$ of the total area $\pi r^2$. Another reason: It is close to a triangle with small base $rd\theta$ and height ______. Integrating $\frac{1}{2}{r}^{2}d\theta$ from $\theta =0$ to $\theta =$ ______ gives the area ______ of a quarter-circle.

This exercise has fill-in blanks from its source book and no answer key.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.7 The Fundamental Theorem and Its Applications, #35