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.
Assuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fP
Find the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.
1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).
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