Find the area between the curve y = 2x(x+2) and the line y = -2x. Find the area between the curve y² = -4x and the line y = -2(x+2) Find the volume of a sphere. Use cylindrical coordinates. Find the volume of a circular cone.

Find the area between the curve y = 2x(x+2) and the line y = -2x. Find the area between the curve y² = -4x and the line y = -2(x+2) Find the volume of a sphere. Use cylindrical coordinates. Find the volume of a circular cone.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 25E

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Question

answer the following by iterated integration in rectangular coordinates.

Find the area between the curve y = 2x(x+2) and the line y = -2x.
Find the area between the curve y² = -4x and the line y = -2(x+2)
Find the volume of a sphere. Use cylindrical coordinates.
Find the volume of a circular cone.

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.

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