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4.4. THE FUNDAMENTAL THEOREM OF CALCULUS
(c) Determine a definite integral whose value tells us exactly the number of minutes
required for the airplane to ascend to 10,000 feet of altitude. Clearly explain
why the value of this integral has the required meaning.
(d) Use the Riemann sum M 5 to estimate the value of the integral you found in (c).
Include units on your result.
4. In Chapter 1, we showed that for an object moving along a straight line with position
function s(t), the object’s “average velocity on the interval [a, b]” is given by
AV [a,b] =
s(b) − s(a)
b − a
.
More recently in Chapter 4, we found that for an object moving along a straight line
with velocity function v(t), the object’s “average value of its velocity function on [a, b]”
is
v AVG[a, b] =
1
b − a
b
a
v(t) dt.
Are the “average velocity on the interval [a, b]” and the “average value of the velocity
function on [a, b]” the same thing? Why or why not? Explain.
4.4. THE FUNDAMENTAL THEOREM OF CALCULUS
(c) Determine a definite integral whose value tells us exactly the number of minutes
required for the airplane to ascend to 10,000 feet of altitude. Clearly explain
why the value of this integral has the required meaning.
(d) Use the Riemann sum M 5 to estimate the value of the integral you found in (c).
Include units on your result.
4. In Chapter 1, we showed that for an object moving along a straight line with position
function s(t), the object’s “average velocity on the interval [a, b]” is given by
AV [a,b] =
s(b) − s(a)
b − a
.
More recently in Chapter 4, we found that for an object moving along a straight line
with velocity function v(t), the object’s “average value of its velocity function on [a, b]”
is
v AVG[a, b] =
1
b − a
b
a
v(t) dt.
Are the “average velocity on the interval [a, b]” and the “average value of the velocity
function on [a, b]” the same thing? Why or why not? Explain.