Changing order of integration Rewrite the following integrals using the indicated order of integration. 24. ∫ 0 1 ∫ 0 1 − z 2 ∫ 0 1 − x 2 f ( x , y , z ) dy dx dz in the order dz dy dx
Changing order of integration Rewrite the following integrals using the indicated order of integration. 24. ∫ 0 1 ∫ 0 1 − z 2 ∫ 0 1 − x 2 f ( x , y , z ) dy dx dz in the order dz dy dx
Solution Summary: The author explains the order of integration of the given integral by using dzdydx.
Changing order of integration Rewrite the following integrals using the indicated order of integration.
24.
∫
0
1
∫
0
1
−
z
2
∫
0
1
−
x
2
f
(
x
,
y
,
z
)
dy dx dz in the order dz dy dx
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.
Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result.
2x
dx
Vx2 + 16
Step 1
2x
To find the definite integral
Vx +
dx, apply the basic integration rule.
+ 16
Let u = x² + 16. Differentiate u in terms of x, du =
A 2 x dx.
Step 2
Rewrite the integration in terms of u.
2x
x = 3
du
V x2 + 16
= xp
Step 3
Apply the power rule of integration.
rx = 3
x = 3
du =
du
+1 1x = 3
+1Jo
1x = 3
Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result.
2x
dx
x2 + 16
Step 1
2x
To find the definite integral
dx, apply the basic integration rule.
+ 16
Let u = x2 + 16. Differentiate u in terms of x, du = 2
2 x dx.
Step 2
Rewrite the integration in terms of u.
2x
du
dx =
V x2 + 16
Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result.
2x
x² + 16
xp
Step 1
2x
To find the definite integral
Vx² +
dx, apply the basic integration rule.
Let u = x² + 16. Differentiate u in terms of x, du =
2 x dx.
Step 2
Rewrite the integration in terms of u.
2x
dx =
du
x² + 16
Chapter 16 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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