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Problem(1) (10 points) Evaluate and approximate $\int_0^2 f(x) dx$ of the functions in Table 1. $\begin{array}{|c|c|c|c|c|c|} \hline f(x) & x^2 & x^4 & 1/(1+x^4) & \sqrt{1+x^2} & sin(\sqrt{x}) & e^{-x^2} \\ \hline \text{Exact value} & 8/3 & 6.400 & & & \\ \hline \text{Left endpoint} & & & & & \\ \hline \text{Right endpoint} & & & & & \\ \hline \text{Trapezoid rule} & & & & & \\ \hline \text{Midpoint rule} & & & & & \\ \hline \end{array}$ Table 1: Choose number of subintervals $n = 16$. Problem(2) (20 points) Evaluate and approximate $\int_0^2 f(x) dx$ of the functions in Table 2. $\begin{array}{|c|c|c|c|c|c|} \hline f(x) & x^2 & x^4 & 1/(1+x^4) & \sqrt{1+x^2} & sin(\sqrt{x}) & e^{-x^2} \\ \hline \text{Exact value} & 8/3 & 6.400 & & & \\ \hline \text{Left endpoint} & & & & & \\ \hline \text{Right endpoint} & & & & & \\ \hline \text{Trapezoid rule} & & & & & \\ \hline \text{Midpoint rule} & & & & & \\ \hline \end{array}$ Table 2: Choose number of subintervals $n = 128$.

          Problem(1) (10 points) Evaluate and approximate $\int_0^2 f(x) dx$ of the functions in Table 1.

$\begin{array}{|c|c|c|c|c|c|}
\hline
f(x) & x^2 & x^4 & 1/(1+x^4) & \sqrt{1+x^2} & sin(\sqrt{x}) & e^{-x^2} \\
\hline
\text{Exact value} & 8/3 & 6.400 & & & \\
\hline
\text{Left endpoint} & & & & & \\
\hline
\text{Right endpoint} & & & & & \\
\hline
\text{Trapezoid rule} & & & & & \\
\hline
\text{Midpoint rule} & & & & & \\
\hline
\end{array}$

Table 1: Choose number of subintervals $n = 16$.

Problem(2) (20 points) Evaluate and approximate $\int_0^2 f(x) dx$ of the functions in Table 2.

$\begin{array}{|c|c|c|c|c|c|}
\hline
f(x) & x^2 & x^4 & 1/(1+x^4) & \sqrt{1+x^2} & sin(\sqrt{x}) & e^{-x^2} \\
\hline
\text{Exact value} & 8/3 & 6.400 & & & \\
\hline
\text{Left endpoint} & & & & & \\
\hline
\text{Right endpoint} & & & & & \\
\hline
\text{Trapezoid rule} & & & & & \\
\hline
\text{Midpoint rule} & & & & & \\
\hline
\end{array}$

Table 2: Choose number of subintervals $n = 128$.

Problem(1) (10 points) Evaluate and approximate ∫0^2 f(x) dx of the functions in Table 1.

f(x) x^2 x^4 1/(1+x^4) √(1+x^2) sin(√(x)) e^-x^2
Exact value 8/3 6.400
Left endpoint
Right endpoint
Trapezoid rule
Midpoint rule

Table 1: Choose number of subintervals n = 16.

Problem(2) (20 points) Evaluate and approximate ∫0^2 f(x) dx of the functions in Table 2.

f(x) x^2 x^4 1/(1+x^4) √(1+x^2) sin(√(x)) e^-x^2
Exact value 8/3 6.400
Left endpoint
Right endpoint
Trapezoid rule
Midpoint rule

Table 2: Choose number of subintervals n = 128.

Added by Cristina M.

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