Evaluate the integral. 8 dx √2 f (x2-1)3/2 Step 1 Recall the Inverse Substitution Rule, where f and g are differentiable functions and g is one-to-one. Â √x) dx = fg dx = [f(g(t)g'(t) f(g(t))g'(t) dt We are given the following. 8 dx (x² - 1)3/2 We note that (x² - 1) 3/2 = (√√x² - 1)³. 3 Expression x2a2 x = a sec(0), 3 If (√√x²-1)³ = (√√x²-a)³. 3 then a = Therefore, the following entry from the Table of Trigonometric Substitutions is appropriate. Substitution Identity 0 ≤ 0 <
Evaluate the integral. 8 dx √2 f (x2-1)3/2 Step 1 Recall the Inverse Substitution Rule, where f and g are differentiable functions and g is one-to-one. Â √x) dx = fg dx = [f(g(t)g'(t) f(g(t))g'(t) dt We are given the following. 8 dx (x² - 1)3/2 We note that (x² - 1) 3/2 = (√√x² - 1)³. 3 Expression x2a2 x = a sec(0), 3 If (√√x²-1)³ = (√√x²-a)³. 3 then a = Therefore, the following entry from the Table of Trigonometric Substitutions is appropriate. Substitution Identity 0 ≤ 0 <
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 21RE
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