For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet, travelled on the interval t = 1 to t = 5?

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For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet, travelled on the interval t = 1 to t = 5?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\int\limits_{1}^{5} \cos(t) dt\]
Solve that ^

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what did you get
careful, you need to put absolute value for "distance"
yeah
1.8
good point, or break up the interval into smaller pieces
find the area under the curve
So......1.8 it is
And dan please give chris his maple syrup
@Ephemera what a lad
@chris00 no man deserves to live without his syrup.
should be around 2.2..
2.2?
Seriously?
i just graphed it...lel
Let's see what @jim_thompson5910 has to say.
|dw:1444450101879:dw|
\[\Large \int_{1}^{5}|\cos(x)|dx\] \[\Large \left|\int_{1}^{\pi/2}\cos(x)dx\right|+\left|\int_{\pi/2}^{3\pi/2}\cos(x)dx\right|+\left|\int_{3\pi/2}^{5}\cos(x)dx\right|\] \[\Large \left|\color{blue}{\int_{1}^{\pi/2}\cos(x)dx}\right|+\left|\color{red}{\int_{\pi/2}^{3\pi/2}\cos(x)dx}\right|+\left|\color{blue}{\int_{3\pi/2}^{5}\cos(x)dx}\right|\] I'll let you finish
1 Attachment
|dw:1444450118173:dw|
the blue areas on the graph can be treated as normal the red area must be forced to be positive
if the question doesn't explicitly say to use algebra, by all means you can use graphical means (says time in an exam) . But always good to use calc techniques.
saves*
2.2 was right

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