University of the Philippines Los Baños College of Engineering and Agro-industrial Technology Department of Engineering Science ENSC 21 - SUPPLEMENTARY MATERIAL COPYRIGHT © 2015 BY JSVENTURA Supplementary Material (Week 1) Trigonometric Substitution Table of Trigonometric Substitutions Expression Substitution Identity − = sin , − 2 ≤ ≤ 2 1 − = + = tan , − 2 < < 2 1 + = − = sec , 0 ≤ < 2 ≤ < 3 2 − 1= Sine substitution Tangent substitution Secant substitution sin = tan = sec = Example: 1. Evaluate ∫ √ . Solution: Let = 3sin , = 3cos 9 − = 9 − 9 = 9 = 3|cos | = 3 cos Thus, we have √ 9 − = 3 cos 9 3cos = = = ( − 1) = − cot − + = − √ − − + 2. Find ∫ √ . Solution: Let = 2 tan , =2