5 Steps to a 5 AP Calculus AB 2019 - William Ma
MA 3972-MA-Book April 11, 2018 15:57 262 STEP 4. Review the Knowledge You Need to Score High Example 4 If ∫k −k f(x)dx= 2 ∫k 0 f ...
MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 263 IfG(x) is an antiderivative of (ex+1) andG(0)=0, findG(1). Answer: ...
MA 3972-MA-Book April 11, 2018 15:57 264 STEP 4. Review the Knowledge You Need to Score High (a) ∫ 0 − 2 g(x)dx (b) ∫− 2 2 g(x)d ...
MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 265 12.7 Solutions to Practice Problems Part A The use of a calculator ...
MA 3972-MA-Book April 11, 2018 15:57 266 STEP 4. Review the Knowledge You Need to Score High Letu= 1 +cosx;du=−sinxdxor −du=sin ...
MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 267 Note thatf(x)=cosx−x^2 is an even function. Thus, you could have wr ...
MA 3972-MA-Book April 11, 2018 15:57 268 STEP 4. Review the Knowledge You Need to Score High 12.8 Solutions to Cumulative Review ...
MA 3972-MA-Book April 11, 2018 15:57 Def inite Integrals 269 x = – 3 x = – 1 y = 1 5 4 3 2 1 11230 1 2 y = – 1 x y Figure 12.8 ...
MA 3972-MA-Book April 11, 2018 16:1 CHAPTER 13 Big Idea 3: Integrals and the Fundamental Theorems of Calculus Areas and Volumes ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 271 13.1 The FunctionF(x)= ∫x a f(t)dt The Second Fundamental Theorem of C ...
MA 3972-MA-Book April 11, 2018 16:1 272 STEP 4. Review the Knowledge You Need to Score High Example 1 IfF(x)= ∫x 0 2 costdtfor 0 ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 273 (a) Evaluate:p(0),p(1),p(4). (b) Evaluate:p(5),p(7),p(8). (c) At what ...
MA 3972-MA-Book April 11, 2018 16:1 274 STEP 4. Review the Knowledge You Need to Score High 0 2 4 6 8 10 12 14 p(x) y x 12 34 56 ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 275 Solution: (a) Sinces= ∫t 0 f(x)dx, thenv(t)=s′(t)=f(t). Thus,v(4)=−8 f ...
MA 3972-MA-Book April 11, 2018 16:1 276 STEP 4. Review the Knowledge You Need to Score High The area under the curve usingnrecta ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 277 Or, find the area of each rectangle: Area of RectI=(f(0))Δx 1 =(1) ( 1 ...
MA 3972-MA-Book April 11, 2018 16:1 278 STEP 4. Review the Knowledge You Need to Score High Or, using ∑ notation: ∑^5 i= 1 f(xi) ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 279 Trapezoidal Approximations Another method of approximating the area un ...
MA 3972-MA-Book April 11, 2018 16:1 280 STEP 4. Review the Knowledge You Need to Score High Area under the curve: ≈ π 4 · 1 2 [ ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 281 Ifx=g(y) is continuous and non-negative on [c,d], then the area under ...
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