The Area of a square,A(t),is increased at a rate
equal to its perimeter ,A(t) satisfies the differential
equation (dA/dt)=
A. 4A B. 2A C.−4(√A) D. 4(√A)
Let f:[0,1]→R be a differentiable function
such that f(f(x))=x for all x∈[0,1] and
f(0)=1.
If n is a positive integer, evaluate the
following integral:
∫_0 ^( 1) (x−f(x))^(2n) dx