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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/02%3A_Multiple_Integration/2.09%3A_Chapter_2_Review_ExercisesThis page presents exercises in multivariable calculus covering integral evaluation, area and volume determination, and center of mass calculations. Problems include confirmations of Fubini's theorem,...This page presents exercises in multivariable calculus covering integral evaluation, area and volume determination, and center of mass calculations. Problems include confirmations of Fubini's theorem, double and triple integrals, and practical applications like Earth modeling and ski resort work estimation. Key answers for selected tasks illustrate results associated with integrals and geometric figures.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_3/04%3A_Multiple_Integration/4.08%3A_Chapter_4_Review_ExercisesConsider a density function with respect to height: the density at the top of the mountain is still density 400 lb/ft3, and the density increases. Assuming a region R, when you revolve...Consider a density function with respect to height: the density at the top of the mountain is still density 400 lb/ft3, and the density increases. Assuming a region R, when you revolve around the x-axis the volume is given by V_x=2πA\overline{y}, and when you revolve around the y-axis the volume is given by V_y=2πA\overline{x}, where A is the area of R. Consider the region bounded by x^2+y^2=1 and above y=x+1.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/15%3A_Multiple_Integration/15.R%3A_Chapter_15_Review_ExercisesConsider a density function with respect to height: the density at the top of the mountain is still density 400\text{ lb/ft}^3, and the density increases. Assuming a region R, when you revolve...Consider a density function with respect to height: the density at the top of the mountain is still density 400\text{ lb/ft}^3, and the density increases. Assuming a region R, when you revolve around the x-axis the volume is given by V_x=2πA\overline{y}, and when you revolve around the y-axis the volume is given by V_y=2πA\overline{x}, where A is the area of R.
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_v2_(Reed)/15%3A_Multiple_Integration/15.R%3A_Chapter_15_Review_ExercisesConsider a density function with respect to height: the density at the top of the mountain is still density 400\text{ lb/ft}^3, and the density increases. Assuming a region R, when you revolve...Consider a density function with respect to height: the density at the top of the mountain is still density 400\text{ lb/ft}^3, and the density increases. Assuming a region R, when you revolve around the x-axis the volume is given by V_x=2πA\overline{y}, and when you revolve around the y-axis the volume is given by V_y=2πA\overline{x}, where A is the area of R.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q4/02%3A_Multiple_Integration/2.09%3A_Chapter_2_Review_ExercisesConsider a density function with respect to height: the density at the top of the mountain is still density 400\text{ lb/ft}^3, and the density increases. Assuming a region R, when you revolve...Consider a density function with respect to height: the density at the top of the mountain is still density 400\text{ lb/ft}^3, and the density increases. Assuming a region R, when you revolve around the x-axis the volume is given by V_x=2πA\overline{y}, and when you revolve around the y-axis the volume is given by V_y=2πA\overline{x}, where A is the area of R. Consider the region bounded by x^2+y^2=1 and above y=x+1.
