I would like these all solved correctly.

1. Evaluate the definite integrals using the Fundamental Theorem of Calculus, Part 1: (a) f: (\\i/E 3\\/E) dt (b) A? sec20d0 (c) [11 1+1x2 d9: 'lof3 2. Draw a graph and use geometrical reasoning to find the area function A(x) that gives the area between the graph of f(t) = 3t 3 and the taxis on the interval [2, x]. Check that A'(a:) = f(x). What theorem are you verifying here? 3. Use the substitution method to find the following indefinite integrals: (a) f d2: (c) /xsin(x2) dz- (b) /1 :29 dx (d) /(a: + a)\" dag for n 7e 1 4. A nuclear reactor dumps radioactive waste into a nearby stream at a rate (in tonnes per year) given by ln(t -l- 1) A' t = H 1 , o _ _ o where t is the number of years that the plant has been in operation. Find the amount, A(t), of radioactive waste that the plant has dumped into the stream after t years of operation. 1' 3+x4 dz. \\/ 5. Use the substitution u = x2 to evaluate the integral / 1