Theta integral 1 to 3 xex2 2x3dx Use Monte Carlo Integrati

Theta = integral 1 to 3 (xe^-x^2 + 2x^3)dx. Use Monte Carlo Integration and the following stream of random numbers between 0 and 1 to compute an estimate for theta. 0.55 0.88 0.53 0.11 0.05 0.08 0.43 0.86 0.21 0.08 0.13 0.32

Solution

Random Numbers Lower limit upper limit f(x) Lower F(x) Upper f(x) Final Value 0.55 0.55 1.65 0.515849978 0.283717488 0.851152 0.567434976 0.88 0.88 2.64 1.514371111 1.332646577 3.99794 2.665293155 0.53 0.53 1.59 0.481395762 0.255139754 0.765419 0.510279507 0.11 0.11 0.33 0.090941081 0.010003519 0.030011 0.020007038 0.05 0.05 0.15 0.04549234 0.002274617 0.006824 0.004549234 0.08 0.08 0.24 0.069196634 0.005535731 0.016607 0.011071461 0.43 0.43 1.29 0.340989921 0.146625666 0.439877 0.293251332 0.86 0.86 2.58 1.426136353 1.226477264 3.679432 2.452954527 0.21 0.21 0.63 0.156507841 0.032866647 0.0986 0.065733293 0.08 0.08 0.24 0.069196634 0.005535731 0.016607 0.011071461 0.13 0.13 0.39 0.104633408 0.013602343 0.040807 0.027204686 0.32 0.32 0.96 0.234280773 0.074969847 0.22491 0.149939695 Sum f(x)= 5.048991836 0.564899197 Divide by 12 0.42074932 Multiply E15 by upper limit(3) 1.262248 Multiply E15 by upper limit(1) 0.420749 Answer 0.841499