Inverse Functions help (1 Viewer)

[BabzBrah]

Hi guys could you please help me with this question

By considering the difference between the area of a rectangle and the area enclosed between the curve y = sin-1 and the y-axis, find the exact area bounded by the curve y = sin-1 , the x-axis and the lines x = 0 and x =√3 / 2.


ANSWER = (√3 .pi) /6 – ½
= ((√3. pi) -3 ) / 6 units ^2

I just get 2, I understand the mentions of the rectangles hinting at something I just don't know what

 

[asianese]

Questions to ask yourself:

What is the y value of the curve y=sin^-1 x when x=sqrt3 / 2 ?

Can you integrate y=sin^-1 x easily?

If not, what is a related function we can use?

What is the area of the curve about the y axis?

What equation would we integrate to get this curve?

What is the relationship between the area of the rectangle, the area you have already found, and the area you ultimately want to find?