Question

$\int_0^8 (x^2 + 1)dx$ A. Sketch a graph of the function and the area represented by the definite integral. B. Estimate the definite integral using left-hand sums with $n = 4$. ($\Delta x = ?$) Is this sum an overestimate or an underestimate of the true value sketched in part A? Explain how you know. C. Estimate the definite integral using right-hand sums with $n = 4$. Is this sum an overestimate or an underestimate of the true value sketched in part A? Explain how you know. D. Estimate the definite integral using trapezoid sums with $n = 4$. Is this sum an overestimate or an underestimate of the true value sketched in part A? Explain how you know. E. Estimate the definite integral using midpoint sums with $n = 4$, Is this sum an overestimate or an underestimate of the true value sketched in part A? Explain how you know. F. Estimate the definite integral using Simpson's rule with $n = 4$. G. Use the Fundamental Theorem of Calculus to evaluate the definite integral. Compare the actual area with your estimates in parts B - F.

          $\int_0^8 (x^2 + 1)dx$
A. Sketch a graph of the function and the area represented by the definite integral.
B. Estimate the definite integral using left-hand sums with $n = 4$. ($\Delta x = ?$) Is this sum an
overestimate or an underestimate of the true value sketched in part A? Explain how you know.
C. Estimate the definite integral using right-hand sums with $n = 4$. Is this sum an overestimate or an
underestimate of the true value sketched in part A? Explain how you know.
D. Estimate the definite integral using trapezoid sums with $n = 4$. Is this sum an overestimate or an
underestimate of the true value sketched in part A? Explain how you know.
E. Estimate the definite integral using midpoint sums with $n = 4$, Is this sum an overestimate or an
underestimate of the true value sketched in part A? Explain how you know.
F. Estimate the definite integral using Simpson's rule with $n = 4$.
G. Use the Fundamental Theorem of Calculus to evaluate the definite integral. Compare the actual
area with your estimates in parts B - F.

∫0^8 (x^2 + 1)dx
A. Sketch a graph of the function and the area represented by the definite integral.
B. Estimate the definite integral using left-hand sums with n = 4. (Δ x = ?) Is this sum an
overestimate or an underestimate of the true value sketched in part A? Explain how you know.
C. Estimate the definite integral using right-hand sums with n = 4. Is this sum an overestimate or an
underestimate of the true value sketched in part A? Explain how you know.
D. Estimate the definite integral using trapezoid sums with n = 4. Is this sum an overestimate or an
underestimate of the true value sketched in part A? Explain how you know.
E. Estimate the definite integral using midpoint sums with n = 4, Is this sum an overestimate or an
underestimate of the true value sketched in part A? Explain how you know.
F. Estimate the definite integral using Simpson's rule with n = 4.
G. Use the Fundamental Theorem of Calculus to evaluate the definite integral. Compare the actual
area with your estimates in parts B - F.

Added by Laura M.

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