Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the following solids. 48. The solid cardioid of revolution D = { ( ρ , φ , θ ) : 0 ≤ ρ ≤ ( 1 − cos φ ) / 2 , 0 ≤ φ π , 0 ≤ θ 2 π }
Volumes in spherical coordinates Use integration in spherical coordinates to find the volume of the following solids. 48. The solid cardioid of revolution D = { ( ρ , φ , θ ) : 0 ≤ ρ ≤ ( 1 − cos φ ) / 2 , 0 ≤ φ π , 0 ≤ θ 2 π }
Solution Summary: The author explains how to find the volume of the given solid in spherical coordinates.
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.
Do the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.
12. [-/1 Points]
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SESSCALCET2 6.3.508.XP.
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Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x + 16
dx
X
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13. [-/1 Points]
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SESSCALCET2 6.3.512.XP.
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Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
dx
8)(2x + 1)
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14. [-/1 Points]
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SESSCALCET2 6.3.518.XP.
Find the area of the region under the given curve from 1 to 5.
y =
x² +7
6x - x²
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SESSCALCET2 6.3.012.
6. [-/1 Points]
Evaluate the integral.
x-4
dx
x²
- 5x + 6
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SESSCALCET2 6.3.019.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x²+1
(x-6)(x-5)²
dx
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SESSCALCET2 6.3.021.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
✓
x²
4
+4
dx
Chapter 16 Solutions
Calculus: Early Transcendentals, Books A La Carte Edition (3rd Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY