Show transcribed image text [11] 1. (a) Write the sigma notation formula for the right Riemann sum Rn of the function f(x) 4 – x2 on the interval [0,2] using n subintervals of equal length, and calculate the definite integral J 2 f(x) dx as the limit of Rn at n → oo (Reminder: Σ k = n(n + 1)/2, Σ k-n (n + 1) (2n + 1)/6 ) に1 に1 (b) Use the Fundamental Theorem of Calculus to calculate the derivative of F(z)- J In(t2 +1) dt (15] 2. Calculate the following indefinite integrals 3 a3 16-x2 dx (b) 22x -4 sec2(z) sec2(z) +3 6] 3. Find the antiderivative F(z) of f(z) such that F(0)-0. 12] 4. Evaluate the following definite integrals (give the exact values, do not approximate): dx (b) c2 cos(nx) dx 0 [6] 5. Find the area enclosed by the graphs of the functions f(z2-3x-5 and g(x)3- x. 3 Bonus question. Given that [f (z) f" (z)] sin xdx = 2 0 and f(T)-1, find f (0)