Question

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.
y = sec^2 x, 0 ≤ x ≤ π/4

Answer 1

To get the area, we use integration. From the graph, we can draw vertical strips that run from 0 to π/4.
∫ y dx
= ∫ sec^2 (x) dx
= tan x | from 0 to π/4
= tan (π/4) - tan (0)
= 1 - 0
= 1

Answer 2

Thank you Jai