Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 7
1. Evaluate
x cosh 3x dx.
Solution: We use integration by parts, and choose u = x, dv = cosh 3x dx so du = dx, v =
cosh 3x dx = 1 sinh 3x. So
3
1
1
sinh 3x
sinh 3x dx
3
3
1
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 5
dx
. [Complete the square.]
6x x2 2
1. Evaluate
Solution:
dx
=
6x x2 2
dx
6x + 2)
dx
=
2 6x + 9 7)
(x
dx
=
7 (x 3)2
du
(u = x 3, du = dx)
=
7 u2
u
x
= arcsin + C
using adx 2
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 8
3x5 3x4 17x3 + 39x2 77x + 81
dx.
(x 2)(x2 + x 6)
1. Evaluate
Solution: Temporarily, we expand the denominator (to make long division easier), so the integrand
is
3x5 3x4 17x3
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 2
1. Find the area enclosed by the x-axis and the curve y = x3 5x2 + 5x 1. Express your answer
in exact form and as simply as possible.
Solution: [Note: a sketch is required, b
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 9
28
1. Determine whether
0
dx
converges or diverges, and if it converges nd its value.
3
x1
Solution: Observe that the line x = 1 is a vertical asymptote of the integrand. By
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 6
1. Evaluate
dx
.
25x2 1
Solution: Let u = 5x. Then du = 5 dx, so
dx
=
25x2 1
dx
(5x)2 1
du
u2 1
1
5
1
= cosh1 u + C
5
1
= cosh1 5x + C.
5
=
2. On the graph of y = cosh x ther
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 3
1. A chain 50 ft long weighing 2 lb/foot hangs over a cli with one end A anchored to the cli.
A cannonball of weight 20 lb is attached to the lower end B. A nylon line of neg
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 4
1. Use logarithmic dierentiation to nd the derivative of
y=
(x3 + 7x2 + 2x + 4)37 cos12 x
.
(ln x)23
Solution: We take logarithms of the absolute values of both sides of the
Math 150b Section 9 First-Year Calculus II Spring 2004
Solutions to Assignment 1
1. Suppose f (x) is dened, for all real x, by
sin x
(24s2 6) ds.
f (x) =
2
Find the maximum and minimum values of f (x), and the values of x where they occur, for x in
the in
Math 15013-09 Spring 2004 Test 3 Name: Soluhoas
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