Finding indefinite integrals In Exercises 31–46, use any basic integration formula or formulas to find the indefinite integral. State which integration formula(s) you used to find the integral. ∫ 1 + e − x 1 + x e − x d x
Solution Summary: The author explains the general logarithmic rule of integrals, which is used to calculate the indefinite integral.
Finding indefinite integrals In Exercises 31–46, use any basic integration formula or formulas to find the indefinite integral. State which integration formula(s) you used to find the integral.
∫
1
+
e
−
x
1
+
x
e
−
x
d
x
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.
Computer giving into girl. Show the algebra necessary to convert the integral into a form where you may use one of your integration formulas.
Solve using Calculus (Integrals).
A swimming pool has the shape of a rectangular box with a base that measures 25 m by 15 m and a uniform depth of 2.5 m. Suppose that the swimming pool is filled with water to the 2 meter mark, how much work is required to pump out all the water to level 3 m above the bottom of the pool.
Density of water: 1000 kg/m3
Solve using Calculus (Integrals).
Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.
∫x2 e5x dx
Chapter 5 Solutions
Calculus: An Applied Approach (MindTap Course List)
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY