Changing the Order of Integration In Exercises 51-60, sketch the region R whose area is given by the iterated integral. Then change the order of integration and show that both orders yield the same area. ∫ 0 1 ∫ − 1 − y 2 1 − y 2 d x d y
Solution Summary: The author explains how to graph the region for the given iterated integral displaystyle
Changing the Order of Integration In Exercises 51-60, sketch the region R whose area is given by the iterated integral. Then change the order of integration and show that both orders yield the same area.
∫
0
1
∫
−
1
−
y
2
1
−
y
2
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.
Converting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/(x2 + y2) over the region 1<= x2 + y2<= e^2.
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
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