The function w() is graphed below. Find the value of each of the following integrals based on the graph of M w(t).. [w(t)dt = 3 w(t)dt 10 √₁² w(t)dt = [0 10 [w(t)dt = 4 w(t)dt -2 L₂w(t [w(t)dt -10 15 2 - [₁₂ w(t)dt = 4 -2 [²5w(t)dt = = -6 X X 8 OF

3. Consider the definite integral x³e-2xdx. Fill in the blanks for the equivalent definite integral after making the variable substitution t = – 2x². Upper bound (1) New Function (2) dt Lower bound (1)

1. A hot metal object is submerged in cold water. The rate at which the object cools (in degrees per minute) is a function f (t) of time. Which quantity is represented by the integral f(t) dt?

EXERCISE A Find the indefinite integral of the following. Show the solution. (50 points) 1. J(2x* — х3 — 2х + 3) dx 2. S(3 – 2x)? dx 3. J3(х — 1)(2 — 3х) dx 4. S(5 – 5* + x5) dx 5. S3 Vy dy 6. Se* dx 7. S(x2 – cos x) dx 8. S(2 sin 0 + 5 cos 0) de 9. S( 1+sinx dx cos?x 10. S(2 cos x – 3 sin x) dx