Please help me with the following question

01: Q3: Preview Consider the function f(x) = (x - 2)3 Preview (a) Estimate the area between the curve y = f(x), the x-axis, BONUS QUESTION. Prove that if f is continuous, then and the lines x = 2 and x = 6, using a Riemann sum with four rectangles (use the right endpoint rule). (b) Calculate the precise area by taking the limit of a Riemann sum. Q2: Preview Elliptic integrals arise in the calculation of the arc length for ellipses, and were first studied by mathematicians and physicists such as Leonhard Euler around 1750. An example is the complete elliptic integral of the second kind, which is defined by 7/2 E(k) = V1 - k2 sin x dx, OSks1. Note that the definite integral is over the variable x, and that the result is a function of k, which is the parameter inside the integral. (a) Consider the elliptic integral for k = 0, that is E(0). Evaluate the definite integral to show that E(0) = 1/2. (b) Consider the elliptic integral for k = 1, that is E(1). Evaluate the definition integral to show that E(1) = 1. (c) Now consider the elliptic integral for k = 2, that is E ( 2 ) . In this case we cannot find an explicit antiderivative to evalute the definite integral using the Fundamental Theorem of Calculus. We can however resort to comparison properties for definite integrais to bound the value of the integral. Starting with the fact that 0