Question

Estimate the area under the graph of y=x^3+3x for x between 0 and 3 . Use a partition that consists of 6 equal subintervals of [0,3] and use the right endpoint of each subinterval as a sample point.

Answer 1

create a table of function values



use either the Trapezoidal Rule, which finds the area of a trapeziod

\[A = h/2 {(f(a) - f(b))}\]

h = 1/2 f(a) = f(0) f(b) = f(1)

this needs to be done 6 times... find the area of 6 trapezoids and add the answers to approximate the area under the curve.

Alternative

Simpsons Rule

Simple form

A \[A = h/6 {f(a) = 4\times f((a+b)/2) + f(b)} \]

the more complex form if

A = h/3( 1st + last + 2 x odds + 4 x evens}

Trapezoidal rule is probably easier