Changing the order of integration Rewrite the following integrals using the indicated order of integration and then evaluate the resulting integral. 42. ∫ 0 4 ∫ 0 16 − x 2 ∫ 0 16 − x 2 − z 2 d y d z d x in the order dz dy dx
Changing the order of integration Rewrite the following integrals using the indicated order of integration and then evaluate the resulting integral. 42. ∫ 0 4 ∫ 0 16 − x 2 ∫ 0 16 − x 2 − z 2 d y d z d x in the order dz dy dx
Changing the order of integrationRewrite the following integrals using the indicated order of integration and then evaluate the resulting integral.
42.
∫
0
4
∫
0
16
−
x
2
∫
0
16
−
x
2
−
z
2
d
y
d
z
d
x
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
Apply integration by parts twice for evaluation the following integrals.
Use a change of variables to evaluate the following indefinite integral.
2x (x -4) 102 dx
Determine a change of variables from x to u. Choose the correct answer below.
O A. u=x?
O B. u= 2x
OC. u=x² - 4
O D. u= (x2-4)10
Write the integral in terms of u.
S2x(6? -4)
102
dx =
du
%3D
Evaluate the integral.
Chapter 16 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
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