In Exercises
19
−
22
, combine the integrals into one integral, then evaluate the integral.
∫
−
1
0
(
x
3
+
x
2
)
d
x
+
∫
0
1
(
x
3
+
x
2
)
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 6 Solutions
MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications
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