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Find the approximations $ L_n $, $ R_n $, $ T_n $, and $ M_n $ for $ n = 5 $, 10, and 20. Then compute the corresponding errors $ E_L $, $ E_R $, $ E_T $, and $ E_M $. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when $ n $ is doubled?

$ \displaystyle \int_1^2 \frac{1}{x^2}\ dx $

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

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