WeBWorK 8 (3.9, 4.1-4.2) And Assignment

WRITTEN ASSIGNMENT 8: ANTI-DERIVATIVES AND
THE DEFINITE INTEGRAL
CALCULUS I, FALL 2022
MATH 1210-090
INSTRUCTOR: WILL FELDMAN
Name: uID:
Problem 1. Find the following anti-derivatives:
(a) Z
x
4 − cos x + x
1/3
dx
(b) Z
x
√
x
2 + 4
dx
Problem 2. A toy rocket launches off of the top of a 10 meter tall platform
at time t = 0. The initial velocity of the rocket is 0 m/s and the acceleration
is given by the following function of time a(t) = 5t + 6 m/s2
for 0 ≤ t ≤ 5
seconds. Find the height of the rocket at t = 5 seconds.
1
2 CALCULUS I, FALL 2022 MATH 1210-090 INSTRUCTOR: WILL FELDMAN
Problem 3. Consider the function
f(x) =



2x − 1 0 ≤ x ≤ 1
3x − 2 1 ≤ x ≤ 3
−14x + 49 3 ≤ x ≤ 5.
sketch the graph of f on the interval x ∈ [0, 5] and use that to help evaluate
the definite integral
Z 4
0
f(x)dx.
Hint: It may help to use the graph to note cancellations between positive
and negative areas and simplify the computation.
Problem 4 (Optional: bonus credit 3 pts). At 6pm a driver enters a toll
road with a speed limit of 80 miles per hour. On entrance they receive a
slip which is stamped with the entry location and time. At 6 : 45pm they
exit through a toll booth 70 miles away and return their slip to pay the toll.
Prove that the driver, at some point during that 45 minutes, was going at
least 10 miles per hour over the speed limit and should receive a speeding
ticket! Hint: Mean value theorem.