Evaluating definite integral with calculator

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 8 what I want to do in this video show you could have also used a graphing calculator to come up with the same result and it would have actually evaluated the ACT the definite integral so let's see how you do that and this what I'm doing here you could do this for a traditional what if we're dealing in Cartesian coordinates rectangular coordinates or for polar course it's really just about evaluating a definite integral so we wanted to evaluate nine times the definite integral from 0 to PI over 4 sine squared theta D theta so how do I do that well I can go to second calculus and I do the FN int that's definite integral so let take use that function and the first thing you want to say well what are you taking the definite integral of and we're taking the definite integral of the definite integral of sine actually I want the parenthesis sine and I could use any variable here as long as I'm consistent with what I am 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 where once again we're assuming X is equal to theta and then the next one you specify what what's the variable you're taking the integral integral with respect to 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 your if you're doing this if you're in Radian mode or that if you're dealing with radians you should assume you're in Radian mode I just did before I died evaluated this we're going between 0 and PI over 4 0 and PI over 4 PI over 4 and then we get so we get this number and then we want to multiply it times 9 so times so my previous answer times 9 press times just as 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 and when we actually evaluate the integral by hand so if we take nine nine pi minus 18 divided by 8 divided by 8 what do we get we get the exact same value so anyway hopefully that's satisfying that you 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