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Section 5-7 : Computing Definite Integrals

7. Evaluate the following integral, if possible. If it is not possible clearly explain why it is not possible to evaluate the integral.

\[\int_{{ - 2}}^{4}{{{x^6} - {x^4} + \frac{1}{{{x^2}}}\,dx}}\] Show Solution

In this case note that the third term will have division by zero at \(x = 0\) and this is in the interval we are integrating over, \(\left[ { - 2,4} \right]\) and hence is not continuous on this interval.

Therefore, this integral cannot be done.