Name:
MATH 230
Spring 2025
Worksheet 1 - Due: Sunday, Jan. 19 at 11:59pm
1. Let g(x) =
Rx
0 f (t) dt, where f is the function whose graph is given below.
(a) Evaluate g(0), g(1), g(2), g(3), and g(6)
(c) Where does g have a maximum value?
(b) On what interval is g increasing?
(d) Sketch a rough graph of g
2. Use part 1 of the Fundamental Theorem of Calculus to find the derivative of the functions.
Z xp
Z ln x
9 − t2 dt
(a) g(x) =
et dt.
(b) y =
3
0
3. Use part 2 of the Fundamental Theorem of Calculus to evaluate the integrals.
Z π
√
Z 4
√
2− x
(b)
(sin x − 3 x) dx.
(a)
dx
2
x
0
1
4. Evaluate the integrals
Z
√
x(x2 + 5x + 2) dx
(a)
Z π
(c)
(2 sin x − 3sec2 x) dx
0
Z 2
(b)
1
1
1
− 3
2
x
x
Z π/4
dt
(d)
sec x tan x dx
0
5. The velocity function of a particle moving along a line is given for v(t) = t2 −3t−18, 0 ≤ t ≤ 6.
Find (a) the displacement and (b) the distance traveled by the particle during the given time
interval.
The problems were obtained from the book Calculus Volume 2 by Strang et al., (OpenStax
1