Changing the Order of Integration In Exercises 61-66, sketch the region of integration. Then evaluate the iterated integral. (Hint: Note that it is necessary to change the order of integration.) ∫ 0 2 ∫ y 2 4 x sin x d x d y
Solution Summary: The author illustrates how to sketch the region of integration of the iterated integral by comparing it with a general double iterative integral.
Changing the Order of Integration In Exercises 61-66, sketch the region of integration. Then evaluate the iterated integral. (Hint: Note that it is necessary to change the order of integration.)
∫
0
2
∫
y
2
4
x
sin
x
d
x
d
y
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.
Converting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/sqrt(x2 + y2) over the region 1<= x2 + y2<= e.
Finding the Volume of a Solid In Exercises 17-20, find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4.y =1/2x3, y = 4, x = 0
using calculus Find the center of mass of the region bounded by the following functions.(a) y = 0, x = 0, y = ln x and x = e(b) y = 2√x and y = x(c) y = sin x, y = cos x, x = 0, and x = π/4.
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY