Area Between Two Curves Using Trigonometry

Question

**Step-by-step.

Find the area of the region enclosed between y=3sin⁡(x) and y=2cos⁡(x) from x=0 to x=0.5pi.

Hint: Notice that this region consists of two parts.

Area = ?

Answer 1

Point of intersection:

3sin(x)=2cos(x)

tan(x)=2/3

x ≈ 0.588 radians

f(x) = 3sin(x)

g(x) = 2cos(x)

Area = ∫^0.588₀ g(x)-f(x) dx + ∫^π/2_0.588 f(x)-g(x)dx

= 2sin(x)+3cos(x)|^0.588₀ -3cos(x)-2sin(x)|^π/2_0.588

I'll let you do the math.