Chapter 5: Q. 8 (page 428)
Suppose v(x) is a function of x. Explain why the integral
of dv is equal to v (up to a constant).
Short Answer
Differentiation and integration are inverse operations of each other.
Chapter 5: Q. 8 (page 428)
Suppose v(x) is a function of x. Explain why the integral
of dv is equal to v (up to a constant).
Differentiation and integration are inverse operations of each other.
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Get started for freeFor each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
Solve the integral:.
Solve the integral
Solve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
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