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welcome to electron line one of the techniques that helps us do line integrals is what we call parametric equations or utilizing parametric equations lets say we want to try to find the area of the circle right here and the circle is defined as x squared plus y squared equals a squared and notice if we pick any point on the circle the distance from there to that from the center to that point will of course be a because the radius is a for the entire circle but the x value of that point will be equal to 8 times the cosine of theta where theta is the angle here and Y will be equal to 8 times the sine of theta so were going to replace X and Y by a cosine of theta and a sine of theta but starting out Im going to say that X were going to write X as a function of Y and of course if we do that the function of Y will be the square root of a squared minus y squared now we can find the area using line integrals by integrating along the complete line right there by saying that the integral a