Notes on Evaluate Integrals using Tables of Integrals - Calculus II | MATH 1920, Study notes of Calculus

Download Notes on Evaluate Integrals using Tables of Integrals - Calculus II | MATH 1920 and more Study notes Calculus in PDF only on Docsity! Integration Using Tables ~ p. 1 J. Ahrens 2000-2006 INTEGRATION USING TABLES Objective: Evaluate integrals using tables of integrals It is frequently necessary to use substitution along with integral tables. It may be necessary to use a formula more than once or to use two or more formulas. Evaluate 22 20 x 12 dx x 4 ⎛ ⎞+ ⎜ ⎟⎜ ⎟+⎝ ⎠ ∫ • The closest formula is # 17: 12 2 du 1 utan C a aa u −= + +∫ • 2 2 2 x 12 81 x 4 x 4 + = + + + • Applying #17 with a = 2: = 22 20 x 12 dx x 4 ⎛ ⎞+ ⎜ ⎟⎜ ⎟+⎝ ⎠ ∫ 2 20 81 dx x 4 ⎛ ⎞+⎜ ⎟+⎝ ⎠∫ = 2 1 1 0 1 xx 8 tan 2 4 tan 1 2 2 2 π− −⎡ ⎤+ = + = +⎢ ⎥⎣ ⎦ Evaluate 2 2 x dx 5 4x− ∫ • The closest formula is #34: 2 2 2 2 1 2 2 u u a udu a u sin C 2 2 aa u − ⎛ ⎞= − − + +⎜ ⎟ ⎝ ⎠− ∫ • Using substitution: let u = 2x udu 2dx and x 2 ⇒ = = 2 2 2 2 u x 1 2dx du 25 4x 5 u ⎛ ⎞ ⎜ ⎟ ⎝ ⎠= − − ∫ ∫ • Using # 34 with : 2a 5= 2 2 2 2 u 1 1 u2 du du 2 85 u 5 u ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = − − ∫ ∫ = 2 11 u 5 u5 u sin C 8 2 2 5 −⎡ ⎤− − + +⎢ ⎥ ⎣ ⎦