Math 2414 Section 7 6 Other Integration Strategies The integration methods studied so far various types of substitutions integration by parts and partial fractions are examples of analytical methods They are done with pencil and paper and give exact results While many important integrals can be evaluated with analytical methods many more integrals lie beyond their reach For this reason other strategies were devised These strategies fall into three categories 1 Tables of Integrals Because there integrals were evaluated analytically be someone else using tables is still considered an analytical method Tables of integrals also contain reduction formulas like those discussed in previous sections 2 Symbolic Methods Computer algebra systems have sophisticated algorithms to evaluate difficult integrals Many definite and indefinite integrals can be evaluated exactly using these symbolic methods 3 Numerical Methods The value of a definite integral can be approximated accurately using numerical methods Numerical means that these methods compute numbers rather than manipulate symbols Computers and calculators often have built in functions to carry out numerical calculations We will concentrate on Tables of Integrals dx Evaluate the integral x 2x 9 x Evaluate 2 6 x dx Find the area of the region bounded by the curve and x p 1 y 1 sin x and the x axis between x 0
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