Chapter 5: Q. 37 (page 464)
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
Short Answer
Part (a) The solution of the integral is
Part (b) The solution of the integral is
Chapter 5: Q. 37 (page 464)
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
Part (a) The solution of the integral is
Part (b) The solution of the integral is
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Explain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
Solve the integral
Suppose v(x) is a function of x. Explain why the integral
of dv is equal to v (up to a constant).
Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withor ? Why do we need to think about the unit circle after trigonometric substitution with ?
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