Realistic Ray Tracing

Homework 1 - Monte Carlo Summation
Homework 2 - Monte Carlo Integration
Homework 3 - Macbeth Color Checker XYZ
Homework 4 - Macbeth Color Checker
Homework 5 - Cornell Box
Homework 6 - Ward BRDF
Homework 7 - Mixture Density
Homework 8 - Participating Medium
Homework 9 - Rayleigh Scattering
Homework 10 - Subsurface Scattering
Homework 11 - Dielectric Material
Homework 12 - Final Image

Homework 2 - Monte Carlo Integration

Use monte carlo summation to estimate (sin^3(x)+cos^3(x)) summed over the interval [0,pie/2], using 100 samples:
pdf1(x) = (24*x^2)/(pi^3)
pdf2(x) = (24*(pi/2 - x)^2)/(pi^3)

uniform sampling = 1.35031
stratify sampling = 1.33284
importance sampling (pdf1) = 1.67693
startify importance (pdf1) = 1.14893
importance sampling (pdf2) = 1.50024
stratify importance (pdf2) = 1.14778
importance sampling (combo) = 1.35171
stratify importance (combo) = 1.33425