The Fundamental Theorem of Calculus is often combined
with and of the previously covered techniques used to evaluate
indefinite integrals.

As in the case with indefinite integrals, one often finds that using substitution works best for functions involving 'x' raised to a power and complex functions. This is one example of using substitution.

There is a key difference when using substitution for definitie integrals - once the substitutions for 'u' are made, there is often no need to replace 'u' with variables in terms of 'x'.

Here we show how to combine the substitution technique with the theorem to evaluate:

$${\int}_{1}^{2}\frac{x\phantom{\rule{5px}{0ex}}dx}{{\left({x}^{2}+2\right)}^{3}}$$

As in the case with indefinite integrals, one often finds that using substitution works best for functions involving 'x' raised to a power and complex functions. This is one example of using substitution.

There is a key difference when using substitution for definitie integrals - once the substitutions for 'u' are made, there is often no need to replace 'u' with variables in terms of 'x'.

Here we show how to combine the substitution technique with the theorem to evaluate:

$${\int}_{1}^{2}\frac{x\phantom{\rule{5px}{0ex}}dx}{{\left({x}^{2}+2\right)}^{3}}$$

Combining Fundamental Theorem and Substitution

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