Students have the option of purchasing the text in a variety of formats. MATH 2A/2B: Calculus: Early Transcendentals by James Stewart, 8th edition or UCI Custom Edition, 8th edition.
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There are also right triangles you can draw to make the connections between x, a, and θ. In each line, the last entry follows from the second entry by one of the Pythagorean identities. X2 − a2 x = a sec θ dx = a sec θ tan θ dθ Here’s a table summarizing the substitution to make in each of the three kinds. The substitution will simplify the integrand since it will eliminate the square root. Kind you substitute for x a certain trig function of a new variable θ. You use them when you see as part of the integrand one of the expressions
For these, you start out with an integral that doesn’t have any trig functions in them, but you introduce trig functions to evaluate the integrals. They’re special kinds of substitution that involves these functions. Now that we have trig functions and their inverses, we can use trig subs. Trigonometric Substitutions Math 121 Calculus II D Joyce, Spring 2013
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