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!

1 Answer
Dee
Oct 4, 2017

#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
enter image source here
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#

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