Practice Problems: Integration by Parts (Solutions)
Written by Victoria Kala
[email protected]
November 25, 2014
The following are solutions to the Integration by Parts practice problems posted November 9.
R
1. ex sin xdx
Solution: Let u = sin x, dv =
1. Obtain the general solution of the differential equation:
y (1-x)dx +x3dy = 0
2. A 96 lb rocket sled is accelerated from rest by a thrust(in pounds force) that varies with time
according to:
F = 3t, if 0t<2sec
F =6, if t2 sec
Determine the equation for
Problem 3G.
A spring-mass-damper system is driven by a triangular wave forcing function as
described by the equation: m)? + RX + sex = f (t) , where
f(t)=A% Z ('1) 23in(o)][2n1]t)
W n=1 (211-1)
See the waveform sketch below. Hint: You know the frequency
Question
two
Question Three
A spherical ball is melting in such a way that its radius is decreasing at the rate of 0.2cm/min. at what
rate is the volume of the snow ball decreasing when the radius is 17cm
V = 4/3 r
Differentiate both sides with respect to
The Intermediate Value Theorem
The theorem states that for any continuous function f(x) within the closed range [a, b],
then there are respective values f(a) and f(b) for the respective points. Any other value lets say c
between points a and b is guarante