00:01
In this question, we are required to draw the graphs for the functions fx is equal to sine x and g x is equal to cosine 2x where x lies between minus pi by 2 and pi by 6.
00:27
And after sketching the graph, we are required to find the area of the region bounded by these two functions.
00:35
So let's see how to solve this question.
00:36
First of all, let's draw the graphs for the functions fx and gx and the graph is shown below.
00:45
So this is the graph for the functions fx and gx.
00:48
This red curve represents function fx and this blue curve represents function gx.
01:00
And now from the available information and the graph, we can observe that gx is greater than equals to fx for x which lies between minus pi by 2 and pi by 6.
01:28
Therefore the expression to calculate the area of the region or the shaded area of the region can be written as a equals to integration minus pi by 2 to pi by 6 g x minus f x that that means cosine 2x minus sine x d x and now let's integrate these two terms.
02:00
So we can write area is equals to and the integration of cosine 2x d x will be equals to sine 2x upon 2 minus the integration of sine x d x will be equals to minus cosine x so here we will have plus cosine x and the limits are minus 5...