Review question

Can we find the area under a parabola? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6067

Question

Let $I(c)=\int_0^1 ((x-c)^2 +c^2)dx$ where $c$ is a real number.

1. Sketch $y=(x-1)^2+1$ for the values $-1\le x\le 3$ and show on your graph the area represented by the integral $I(1)$.

2. Without explicitly calculating $I(c)$, explain why $I(c) \ge 0$ for any value of $c$.

3. Calculate $I(c)$.

4. What is the minimum value of $I(c)$ (as $c$ varies)?

5. What is the maximum value of $I(\sin \theta)$ as $\theta$ varies?