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Use the Midpoint Rule with [math]n=4[/math] to compute approximations to the following integrals. In \ref{ex8.3.1a}, \ref{ex8.3.1b}, \ref{ex8.3.1c}, \ref{ex8.3.1d}, and \ref{ex8.3.1e} compare the result obtained with the true value.

• lab{8.3.1a} [math]\int_0^1 (x^2+1)\;dx[/math]
• lab{8.3.1b} [math]\int_{-1}^3 (6x-5)\;dx[/math]
• lab{8.3.1c} [math]\int_1^3 \frac1{x^2} dx[/math]
• lab{8.3.1d} [math]\int_0^3 \frac1{1+x} dx[/math]
• lab{8.3.1e} [math]\int_0^3 \sqrt{1+x}\;dx[/math]
• [math]\int_0^{2\pi} \sin^2x\;dx[/math]
• [math]\int_0^1 e^{-x^2} dx[/math]
• lab{8.3.1h} [math]\int_0^1 \sqrt{1+x^3}\; dx[/math].