Use the Trapezoidal Rule with n=4 to approximate the definite integral.

Question

Use the Trapezoidal Rule with n=4 to approximate ∫(-2 to 2)(x³dx)

Answer 1

Regardless of the approximation, you can tell by looking at this that since the function is odd, the exact area is 0. But, we can use the rules to see how it works.

f(-2) = -8

f(-1) = -1

f(0) = 0

f(1) = 1

f(2) = 8

Area of a Trapezoid = 1/2(a+b)(h) In this case, the height of each is 1 due to -2 to 2 split into 4. Use the functions values for each a and b.

1/2(1)[(-8+-1)+(-1+0)+(0+1)+(1+8)]

1/2(1)[-9 + -1 + 1 + 9] = 0