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)

∫ x4 − cosx+ x1/3 dx

(b)

∫ x√

x2 + 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 ∫ 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.