Changing the Order of Integration In Exercises 25–30, sketch the solid whose volume is given by the iterated integral. Then rewrite the integral using the indicated order of integration. ∫ 0 1 ∫ y 1 ∫ 0 1 − y 2 d z dx dy Rewrite using d z d y d x
Changing the Order of Integration In Exercises 25–30, sketch the solid whose volume is given by the iterated integral. Then rewrite the integral using the indicated order of integration. ∫ 0 1 ∫ y 1 ∫ 0 1 − y 2 d z dx dy Rewrite using d z d y d x
Solution Summary: The author calculates the Triple integral in the indicated order of integration, which is dzdydx.
Changing the Order of Integration In Exercises 25–30, sketch the solid whose volume is given by the iterated integral. Then rewrite the integral using the indicated order of integration.
∫
0
1
∫
y
1
∫
0
1
−
y
2
d
z
dx dy
Rewrite using
d
z
d
y
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.
Use triple integration to find the volume of the tetrahedron T shown in Figure 2. Then find the
coordinates of the centroid.
(0, 0, 1)
(1, 0, 0)
Figure 2
(0, 1, 0)
Converting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/sqrt(x2 + y2) over the region 1<= x2 + y2<= e.
In Exercises 33–46, sketch the region of integration and write anequivalent double integral with the order of integration reversed.
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