I've got a question that was on my exam and I got it wrong after literally 10 attempts.
The question is: Find the area bounded by y=sin x and y=cos 2x for π/6 ≤ x ≤ 5π/6
Thanks!
Hey Simona! Welcome to the forums!!
Let's have a look.
The first step for an area question of this nature is to draw a quick sketch, just to get a better picture of what we are dealing with. Wolfram Alpha helped me out here, but you don't need any great level of accuracy, we just want the position of the curves with relation to each other.
Note also that this sketch from Wolfram Alpha has the axes centred at the first point of intersection, totally irrelevant to this question, just ignore the coordinates! Okay! So it is clear from a quick sketch that the sinx curve is above the cos2x curve in this domain.
There is a really neat trick here. Even when the curves go above or below the x axis, any weird combination, we can
always find the area by finding the area under the upper curve and subtracting the area under the lower curve, in the given domain. It's nice, and eliminates the need for weird sums of absolute values of integrals. Literally, the integral of the upper curve subtract the integral of the lower curve, works every time
So, the working would be:
I hope this helps!!