1. Use the Antiderivatives and Definite Integrals Theorem to evaluate the following integrals. a. 4x dx b. 4x dx c. 4x dx d. Does 4x dx = 4x dx - S 4x dx ? (yes or no) 2. (10 points) The velocity of a car after t seconds is (27 - t) feet/sec. ( a. Plot the velocity vs time for t>= 0. b. How many seconds does it take for the care to come to a stop (velocity = 0)? c. How far does the car travel while coming to a stop? d. How many seconds does it take the car to travel half the distance in part (c)? Hint: Solve for t using the Desmos graphing program. 3. (10 points) Verify that F(x) is an antiderivative of the integrand f(x) by differentiating F(x). a. Let F(x) In(1+x) Compute f(x) F'(x). b. Then use Part 2 of the Fundamental Theorem to evaluate the definite integral. Let a = 1 and b = 4 in F(a) and F(b) in the following integral. ff(x)dx = F(b) - F(a) c. Check your answer using the Desmos graphing program. 2x For your first entry, enter "f(x)= 33 1+x2 For your second entry enter "int 1 4 f(x) dx" Show a screen shot. d. Do your answers from (b) and (c) match? (yes or no) 4. (10 points) Using Leibniz's Rule ((t)dt find