5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:52 242 STEP 4. Review the Knowledge You Need to Score High Answer:Rewrite as ∫ x(x^2 −1)^1 /^2 dx ...

MA 3972-MA-Book May 8, 2018 13:52 Integration 243 If dy dx =ex+2 and the point (0, 6) is on the graph ofy, findy. ∫ − 3 ex ...

MA 3972-MA-Book May 8, 2018 13:52 244 STEP 4. Review the Knowledge You Need to Score High 11.6 Solutions to Practice Problems 1. ...

MA 3972-MA-Book May 8, 2018 13:52 Integration 245 Letu= 1 x ;du= − 1 x^2 dxor−du = 1 x^2 dx. Rewrite: ∫ sec^2 u(−du)=− ∫ sec^2 ...

MA 3972-MA-Book May 8, 2018 13:52 246 STEP 4. Review the Knowledge You Need to Score High Sincef(x) is the antiderivative of 1 ...

MA 3972-MA-Book April 11, 2018 15:57 CHAPTER 12 Big Idea 3: Integrals and the Fundamental Theorems of Calculus Definite Integral ...

MA 3972-MA-Book April 11, 2018 15:57 248 STEP 4. Review the Knowledge You Need to Score High 12.1 Riemann Sums and Definite Inte ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 249 Example Evaluate ∑n i= 1 i(i+1) n . Rewrite: ∑n i= 1 i(i+1) n as 1 ...

MA 3972-MA-Book April 11, 2018 15:57 250 STEP 4. Review the Knowledge You Need to Score High 2 c 1 c 2 x 1 x 0 = 0 y x 2 x 3 x c ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 251 Example 1 Use a midpoint Riemann sum with three subdivisions of equ ...

MA 3972-MA-Book April 11, 2018 15:57 252 STEP 4. Review the Knowledge You Need to Score High Iff(x),g(x), andh(x) are integrable ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 253 The remaining properties are best illustrated in terms of the area ...

MA 3972-MA-Book April 11, 2018 15:57 254 STEP 4. Review the Knowledge You Need to Score High Set 2k^2 +k− 6 = 30 ⇒ 2 k^2 +k− 36 ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 255 Example 1 Evaluate ∫π π/ 4 cos(2t)dt. Letu= 2 t;du= 2 dtor du 2 =dt ...

MA 3972-MA-Book April 11, 2018 15:57 256 STEP 4. Review the Knowledge You Need to Score High Letu=x^2 ; then du dx = 2 x. Rewrit ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 257 12.3 Evaluating Definite Integrals Main Concepts:Definite Integrals ...

MA 3972-MA-Book April 11, 2018 15:57 258 STEP 4. Review the Knowledge You Need to Score High Example 3 Evaluate ∫− 1 − 8 ( √ (^3 ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 259 Example 2 Evaluate ∫ 4 0 ∣∣ x^2 − 4 ∣∣ dx. Setx^2 − 4 =0;x=±2. Thus ...

MA 3972-MA-Book April 11, 2018 15:57 260 STEP 4. Review the Knowledge You Need to Score High Rewrite the indefinite integral: ∫ ...

MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 261 Definite Integrals Involving Odd and Even Functions Iff is an even ...