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## Area defined by polar graphs

Current time:0:00Total duration:2:59

# Evaluating definite integral with calculator

## Video transcript

- [Voiceover] In the last
video, we tried to find the area of the region, I
guess this combined area between the blue and this
orange, the area, I guess the overlap between these two
circles and we came up with nine pi minus 18 all of that over eight. What I want to do in this
video, you could have also used a typical graphing
calculator to come up with the same result, and
it would have actually evaluated the definite integral. So let's see how you do that. Now this, what I'm doing
here, you could do this for a traditional, what if
you're dealing with Cartesian coordinates, rectangular coordinates, or for polar coordinates,
cause it's really just about evaluating the definite integral. So we wanted to evaluate nine
times the definite integral from zero to pi over four
sin squared theta d theta, so how do I do that? Well I can go to second,
calculus, then I do the F N INT, that's definite integral. So let's use that function,
and then the first thing, you want to say "well, what are you taking "the definite integral of?" And we're taking the
definite integral of... Sine, actually I want
the parentheses, sine, and I could use any variable
here, as long as I'm consistent with what I'm
integrating with respect to. So I tend to use just the "x" button, because there is an "x" button, but we'll just assume that
in this case x is theta. So sine of x squared, instead
of sine of theta squared, we're once again assuming
that x is equal to theta. And then the next one, you specify, "Well what's the variable you're taking "the integral with respect to?" In this case it's x, if
we'd put in a theta here then we would want to put
a theta there as well. And then you want the
bounds of integration, and you should assume
that your calculator, or if you're doing this,
if you're in radiant mode, or if you're dealing with
radiants, you should assume you're in radiant mode, I just
did before I evaluated this. We're going between zero and pi over four. Zero and pi over four. And then, we get... So we get this number, and then we wanted to
multiply it times nine. So my previous answer times nine. If I just press times, it does this, "Previous answer times" nine, is equal to this number, one point two eight four two nine. So let's verify that
that's the same exact value we got when we actually
evaluated the integral by hand. So if we take nine, nine pi
minus 18 divided by eight, divided by eight, what do we get? We get the exact same value. So anyway, hopefully that's satisfying, that we got the same value either way, and a little exposure for
how you might be able to evaluate some integrals
using a calculator, which can be useful
when you can't actually evaluate them analytically.