Answer:
-1.1857
Explanation:
Symbolic form of trapezoidal rule
integral_(-1.88988)^1.88988 (x^3 + cos(x)) dx≈(1.88988 - (-1.88988))1/2 (-7.0637 + 6.4363)
Exact integral result
2 sin(108316202/57313751) ≈ 1.899045542542963
Method comparisons
method | result | absolute error | relative error
left endpoint | -26.6991 | 28.5982 | 15.0592
right endpoint | 24.3277 | 22.4287 | 11.8105
midpoint | 3.77976 | 1.88072 | 0.990349
trapezoidal rule | -1.1857 | 3.08475 | 1.62437
Simpson's rule | 2.12461 | 0.225562 | 0.118776
Boole's rule | 1.89403 | 0.00501286 | 0.00263967
(over the range from -1.88988 to 1.88988 and using 1 interval)