Name
Integration
byRParts
R
udv = uv − vdu
1. Use
Z integration by parts to find the integrals
(a) x ln(x)dx
Z
(b)
−6x2 cos(8x)dx
2. Find the area between y = (x − 2)ex and the x-axis from x = 2 to x = 4
The average value of a function on the interval [a, b] is
Z b
1
f (x)dx
b−a a
provided the indicated definite integral exists.
3. The intensity of the reaction to a certain drug, in appropriate units is given
by R(t) = te−0.1t . Where t is time (in hours) after the drug is administered. Find the
average intensity during the second hour.
4. Determine whether the improper integrals below converge or diverge, and find
the value of each that converges.
Z ∞
1
√ dx
(a)
x
1
Z
0
4ex dx
(b)
−∞
Z
(c)
0
∞
1
dx
(x + 1)2
1