00:01
This problem is a little bit different from a more straightforward problem where we're finding just the area under a curve.
00:08
In this problem, we're given two functions, and we have to find it what value of c would the area be enclosed by both of these functions.
00:19
So the functions were given is y equals cosine x and y equals the cosine of x minus c.
00:26
So the first thing that i did was i graphed it so we can visualize where these curves are moving and where they're hitting on the x and y axis.
00:40
So now what we can do is we can see from this graph that the function cosine of x minus c crosses the x axis where x equals pi over 2 plus c.
00:53
Now this is very helpful because now we can use that to construct an integral.
00:58
Because remember, we're using our techniques of integration to find this value of c.
01:04
So we would get the integral from 0 to c over 2 of cosine of x minus the cosine of x minus x minus c in dx.
01:15
So then we can do a little bit of substitution to find that this integral is the same thing as saying the negative integral of pi over 2 plus c to c of cosine of x minus c and d.
01:29
And then what we would do is we would simply take the antiderivative and we would get sign of x minus sign of x minus c and we'll evaluate that from zero to c over two...