Calc Solutions: Red Herring Integral (Online calculus course test homework solutions)

Wednesday, February 22, 2012

Red Herring Integral (Online calculus course test homework solutions)

Question: What is the value of the integral to 2 decimal places.

$\int_{6}^{41}{\frac{x^{1.9}+72}{x}dx}$

Solution: This problem is a red herring, or rather, a trick, because it seems like we should have to do partial fractions or some complicated maneuver to turn this into something we can easily antidifferentiate, but the trick is actually quite trivial:

$\int_{6}^{41}{\frac{x^{1.9}+72}{x}dx}=\int_{6}^{41}{\frac{x^{1.9}}{x}dx}+\int_{6}^{41}{\frac{72}{x}dx}=\int_{6}^{41}{x^{.9}dx}+\int_{6}^{41}{\frac{72}{x}dx}$

And these are two integrals that should be familiar, so we get:

$=[\frac{x^{1.9}}{1.9}+72ln(x)]_{6}^{41}=718.565248\approx718.57$
as required.

Calc Solutions

Wednesday, February 22, 2012

Red Herring Integral (Online calculus course test homework solutions)

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