Question

Sketch the region enclosed by the given curves and find its area.

y = sec^2 x,     y = 8 cos x,      - π/3 ≤ x ≤ π/3

Answer 1

Step 1:

The curve equations are and and .

Graph the curves and .

Observe the graph:

The area of the region is 10.383 sq-units.

Step 2:

Area of the region is .

Observe the graph:

Upper curve is .

Lower curve is .

Area of the region is 10.392 sq-units.

Solution:

Region enclosed by the curves and is

Area of the region is 10.392sq-units.