Find the area between the graphs of fx 4 - x2 gx x 2 on

Question

1. The velocity of a car after t seconds is 20-2t feet per second. (a) How many seconds does it take for the car to come to a stop (velocity = 0)? (b) How far does the car travel while coming to a stop? (c) How many seconds does it take the car to travel half the distance in part (b)?

2. Let A(x) = ₁∫^x √(cos²t+1) dt, find A'(x) at x=0,and π/2.

3. Evaluate the following definite integrals:

(a)  -₁∫²(-3x² + 6x + 2)dx

(b) ₁∫⁹√x dx

4. Evaluate the following indefinite integrals.

(a) ∫(-4x3 + e3x - √2) dx

(b) ∫(x² - 2)(x³ + 2) dx 

5. Evaluate the integrals by making appropriate substitutions.

(a) ∫x√(3x²+4) dx                                                                             

(b) ∫cos³x sinx dx 

6. Find the area between the graphs of f(x) = 4 - x², g(x) = x + 2, on the interval 0 ≤ x ≤ 2.

7. Find the area of the closed region bounded above by the graph of f(x) = 2 - x² and below by the graph of g(x) = - 2.