Question

Trig and Integration help please?

Find, to one decimal place, the area bounded by `x=0`, `y=0`, `y=cosx` and `y=cos^-1x`.

Thanks!

Answer 1

`int_0^0.74 cos(x)d\x +int_0.74^1arccos(x)d\x = 0.8`

Explanation:

The plot of `cos(x)` in purple and `cos^{-1}(x)` in blue

The coordinate of intersection `(x,y) = (0.74,0.74)`
So, between `(0,0.74)`,`cos(x)` is the bounding function on the upper part, while between `(0.74,1)`, `cos^{-1}(x)` is the bounding function.
Therefore the area of interest is:
`int_0^0.74 cos(x)d\x +int_0.74^1arccos(x)d\x = 0.8`