Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Chapter 7, Problem 1PE
To determine
The method of
Expert Solution & Answer
Explanation of Solution
The method of integration by substitution or change of variables is based on the chain rule for derivatives.
The method
The steps for using substitution for integration for indefinite integral are given below.
- Calculate the derivative of u and solve it for it for dx .
- Substitute the expression for u and dx in the original integral.
- Eliminate the variable x and leave the integral in u only.
- Simplify the integral.
- Integrate the integral.
- Again, substitute the value of u in the expression.
The steps for using substitution for solving a definite integral are same but the limits of the integration are also needed to changed according to the substitution.
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Chapter 7 Solutions
Student's Solution and Survival Manual for Calculus
Ch. 7.1 - Prob. 1PSCh. 7.1 - Prob. 2PSCh. 7.1 - Prob. 3PSCh. 7.1 - Prob. 4PSCh. 7.1 - Prob. 5PSCh. 7.1 - Prob. 6PSCh. 7.1 - Prob. 7PSCh. 7.1 - Prob. 8PSCh. 7.1 - Prob. 9PSCh. 7.1 - Prob. 10PS
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- 6. The largest interval in which the solution of (cos t)y′′ +t^2y′ − (5/t)y = e^t/(t−3) , y(1) = 2, y′(1) = 0is guaranteed to exist by the Existence and Uniqueness Theorem is:A. (0, ∞) B. (π/2, 3) C. (0,π/2) D. (0, π) E. (0, 3)arrow_forward12. For the differential equation in the previous question, what is the correct form for a particularsolution?A. yp = Ae^t + Bt^2 B. yp = Ae^t + Bt^2 + Ct + DC. yp = Ate^t + Bt^2 D. yp = Ate^t + Bt^2 + Ct + D Previous differential equation y′′ − 4y′ + 3y = e^t + t^2arrow_forward16. The appropriate form for the particular solution yp(x) of y^(3) − y′′ − 2y′ = x^2 + e^2x isA. yp(x) = Ax^2 + Bx + C + De^2x B. yp(x) = Ax^3 + Bx^2 + Cx + Dxe^2xC. yp(x) = Ax^2 +Be^2x D. yp(x) = A+Be^2x +Ce^−x E. yp(x) = Ax^2 +Bx+C +(Dx+E)e^2xarrow_forward
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Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Evaluating Indefinite Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=-xHA2RjVkwY;License: Standard YouTube License, CC-BY
Calculus - Lesson 16 | Indefinite and Definite Integrals | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=bMnMzNKL9Ks;License: Standard YouTube License, CC-BY