The region between the curves and use the calculator to compute the area correct to five decimal places.
Area = 0.25142
Graph the two curves and set up the integral for the area using the concept of the area between the two curves.
Area between two curves:
The area between the curves y=fxand y=g(x) and between x=a and x= b, where f a nd g are the continuous functions is
A= ∫ab|fx-gx| dx
The equation of the curves y=tan2x and y=x
Graph g(x)=tan2x and f(x)=x on a calculator
The curves intersect at x =0 and x=0.74936
So, the area is given by ∫00.74936(x-tan2x) dx
Evaluate the integral using a calculator.