Using the convolution integral method, find the probability of failure and generalized reliability index of a basic component with the following probability density functions for load and resistance.
The resistance R has Rayleigh distribution:
fa(r) = 2r exp(-r^2), r > 0
and the load S has exponential distribution:
fs(s) = exp(-s/70), s > 0
R and S are probabilistically independent.
You may use numerical integration to evaluate the final integral, but make sure you document clearly how you set up the problem and what integral you are evaluating.