Find the area enclosed by the given curves

Question

y = 8 cos(𝜋x),    y = 8x² − 2

Answer 1

Plotting the two equations, the equations intersect at ±0.5.

8cos(π/2) = 8(1/4)-2 = 2-2

0 = 0

Using symmetry, we can evaluate the area enclosed by the two curves as:

A = 2∫₀^0.5 8cos(πx) - 8x²+2 dx

= 2[8sin(πx)/π - 8x³/3 + 2x]₀^0.5

= 2[8/π-(8/3)(1/8)+1 - 0 - 0 +0] = 16/π - 2/3 + 2 ≈ 6.42629