Math 141H Homework 1 (Section 6.1. Work) Solution
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1. Find the volume of the solid whose base is the region given by the ellipse 4x2 + y 2 = 1 such that
(1) each
Math 141H Homework 3 Solution (Section 6.2, 6.7 and 6.8)
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1. Find the length of the curve that can be represented as the graph of the function f (x) =
on the inte
Math 141H Homework 5 Solution (Section 7.1-7.3)
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1. Find the inverse of f (x) =
Solution:
y=
ex 1
.
ex + 1
ex 1
ey 1
1+x
= x = y
= xey + x = ey 1 = ey =
.
ex + 1
Homework 6 Solution (Section 7.5 and 7.6)
Show oil your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Compute
(1)003 (sirr1 , (2) sin (tan"1(\/E))
Soiuiion (1) Let 6 = sin1 Then, sine = Therefore,
cos (sin'1 =
Math 141H Homework 7 Solution (Section 8.1)
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1. Compute the integral
2
(1)
e2
x sin xdx,
1
x2 ln xdx,
(2)
0
x 2x dx
(3)
1
0
e
(ln x)2 dx,
(4)
x sec2 xdx,
(5)
(6)
Math 141H Homework 9 (Section 8.4 and 8.6) Solution
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1. Find the integral
(1)
x2
dx
x2 1
x2 1 + 1
1
x2
=
=1+ 2
21
21
x
x
x 1
Solution:
x2
x2
dx = x +
x2 1
=
1
1
1
Math 141H Homework 10 Solution (Section 8.7)
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Determine whether the following improper integrals converge. If convergent, nd the value.
3
dx
4 + x2
(1)
1
1
dx