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Math 148.05A - Review for Final - Chapter 14: Integration
(1) What is the relationship between an indefinite integral of a function f (x) and an antiderivative of f (x)?
(2) Given a particular
function f (x), how many indefinite integrals does it have?
R 0
(3) What is f (x) dx?
R
(4) If v(t)R is the velocity of an object at time t, what is v(t) dt?
(5) Find e√5x dx.
R 1+√x
√
dx.
(6) Find
R 1 x 2x
(7) Find 0 (x2 +1) ln(x2 +1) dx.
R3
(8) Draw a diagram of the area given by the integral 1 x1 dx.
(9) What is the fundamental theorem of calculus? Why is it important?
2
(10) If marginal revenue is M R(q) = q 2 + q+1
, what is the revenue function r(q)?
(11) Find the area between the curves x = 1 − y 2 , y = x − 1 and y = 2.
1
(12) If marginal cost is (q+1)
2 , find the change in costs if you change production from q = 5 to
q = 6.
(13) A falling object is acted upon only by the force of gravity, so its acceleration is given by
a(t) = −9.8 m/s2 . After 5 seconds, the object hits the ground (i.e. height 0) moving at a
velocity of −40 m/s (the minus sign indicates that the object is moving downwards). Find
a formula for h(t), the height of the object at time t. What is the initial velocity of the
object?