Blog: `f(x) = 2 sin(x) - sin(2x), [0, pi]` Find the average value of the function on the given interval.

Friday, October 23, 2015

$\displaystyle{f{{\left({x}\right)}}}={2}{\sin{{\left({x}\right)}}}-{\sin{{\left({2}{x}\right)}}},{\left[{0},\pi\right]}$ Find the average value of the function on the given interval.

The average value on an interval is the integral on this interval divided by the length of the interval.

The length is $\displaystyle\pi$ . The integral is

$\displaystyle{\left(-{2}{\cos{{\left({x}\right)}}}+\frac{{1}}{{2}}{\cos{{\left({2}{x}\right)}}}\right)}{{\mid}_{{0}}^{\pi}}={2}+\frac{{1}}{{2}}+{2}-\frac{{1}}{{2}}={4}.$

So the average value is $\displaystyle\frac{{4}}{\pi}.$

The average value on an interval is the integral on this interval divided by the length of the interval.

The length is $\displaystyle\pi$ . The integral is

$\displaystyle{\left(-{2}{\cos{{\left({x}\right)}}}+\frac{{1}}{{2}}{\cos{{\left({2}{x}\right)}}}\right)}{{\mid}_{{0}}^{\pi}}={2}+\frac{{1}}{{2}}+{2}-\frac{{1}}{{2}}={4}.$

So the average value is $\displaystyle\frac{{4}}{\pi}.$

Blog

Friday, October 23, 2015

$\displaystyle{f{{\left({x}\right)}}}={2}{\sin{{\left({x}\right)}}}-{\sin{{\left({2}{x}\right)}}},{\left[{0},\pi\right]}$ Find the average value of the function on the given interval.

No comments:

Post a Comment

What is the Exposition, Rising Action, Climax, and Falling Action of "One Thousand Dollars"?

Friday, October 23, 2015

Find the average value of the function on the given interval.

No comments:

Post a Comment

What is the Exposition, Rising Action, Climax, and Falling Action of &quot;One Thousand Dollars&quot;?

$\displaystyle{f{{\left({x}\right)}}}={2}{\sin{{\left({x}\right)}}}-{\sin{{\left({2}{x}\right)}}},{\left[{0},\pi\right]}$ Find the average value of the function on the given interval.

What is the Exposition, Rising Action, Climax, and Falling Action of "One Thousand Dollars"?