# How do you find the error that occurs when the area between the curve y=x^3+1 and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4?

Assuming that you want the actual error, use the fundamental theorem of calculus to get the exact value of ${\int}_{0}^{1} \left({x}^{3} + 1\right) \mathrm{dx}$ Then find the difference (subtract) from the trapezoid approximation.
int_0^1(x^3+1)dx=(x^4/4+x)]_0^1=(1/4+1)-(0)=4/5=1.25.
The trapezoid rule with $n = 4$ gives $1.265625$
The error, then is $0.015625$.