7. ASSIGNMENT 6: 1ST FUNDAMENTAL THEOREM OF CALCULUS Problem 7.1. Calculate the following derivative: dx -x2 arctan(2) Problem 7.2. Calculate the following derivative: 7.5 cos(13) -13 sin(12 ) Problem 7.3. Calculate the following derivative: sin(u?) dx du r=ro u Why are the involved functions Riemann integrable? Problem 7.4. Consider a Riemann Integrable function f. Calculate the values of a, b, c in each of the following: [ f(10 -V25 )da = a f(3x - V3) dx. [ f(-32 + 1)de = a / f(x -3)dz. Problem 7.5. Prove that the function f(x) = or + 8 is Riemann inte- grable over [a, b] and calculate its Riemann integral over [C, D]. (Use limits of Riemann sums