Consider the function
f(x)=x51−x6,0≤x<1.
Answer the following:
a. Part 1: (i) Show that the integral I=∫x51−x6dx can be rewritten in terms of a single variable raised to a power.
b. Part 2: (ii) Hence evaluate I in its simplest form.
c. Part 3: (iii) Using the result of part (ii), find the exact value of ∫0621x51−x6dx.