Riemann Sum Approximation Error

Question

A student approximates the area under the curve of $$f(x)=3*x^2+2*x+1$$ on the interval [0,3] using Riemann sums. The student chose only 3 large subintervals and obtained an area that is significantly different from the true value. What mistake did the student make in the experimental process?

Accepted Answer

Choosing an inadequate number of subintervals for the Riemann sum, which resulted in a significant approximation error.

Answer

Failing to square the $$x$$ terms correctly during integration, resulting in an erroneous area.

Answer

Incorrectly applying the Fundamental Theorem of Calculus by missing a constant of integration.

Answer

Using the midpoint Riemann sum instead of the trapezoidal rule, leading to less precision in the area calculation.