Question

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)

The integral of e^(3sqrt(t)) sin3t dt from 0 to 4. n=8

Answer 1

we want to approximate

∫[0,4] e^(3√t) sin 3t dt

So, divide the interval[0,4] into 8 pieces, each of width 0.5

Now apply each Rule named above, calculating f(x) for each value from 0 to 4, and add up the areas of all the rectangles or trapezoids.

There are online calculators for each of the Rules.