5 Steps to a 5 AP Calculus BC 2019
242 STEP 4. Review the Knowledge You Need to Score High Example 3 Evaluate ∫− 1 − 8 ( √ (^3) y+ 1 √ (^3) y ) dy. Rewrite: ∫− 1 − ...
Definite Integrals 243 Example 2 Evaluate ∫ 4 0 ∣∣ x^2 − 4 ∣∣ dx. Setx^2 − 4 =0;x=±2. Thus ∣∣ x^2 − 4 ∣∣ = { x^2 −4ifx≥2orx≤− 2 ...
244 STEP 4. Review the Knowledge You Need to Score High Rewrite the indefinite integral: ∫ csc^2 u du 3 =− 1 3 cotu+c =− 1 3 cot ...
Definite Integrals 245 Definite Integrals Involving Odd and Even Functions Iff is an even function, that is,f(−x)=f(x), and is c ...
246 STEP 4. Review the Knowledge You Need to Score High Example 4 If ∫k −k f(x)dx= 2 ∫k 0 f(x)dxfor all values ofk, then which o ...
Definite Integrals 247 Example 1 Evaluate ∫∞ 1 1 x dx. ∫∞ 1 1 x dx=limk→∞ ∫k 1 1 x dx=limk→∞[lnx]k 1 =limk→∞(lnk)=∞so the integr ...
248 STEP 4. Review the Knowledge You Need to Score High 11.5 Rapid Review Evaluate ∫x π/ 2 costdt. Answer: sint]xx/ 2 =sinx−si ...
Definite Integrals 249 11.6 Practice Problems Part A The use of a calculator is not allowed. Evaluate the following definite int ...
250 STEP 4. Review the Knowledge You Need to Score High Use a midpoint Riemann sum with three subdivisions of equal length to fi ...
Definite Integrals 251 11.8 Solutions to Practice Problems Part A The use of a calculator is not allowed. 1. ∫ 0 − 1 ( 1 +x−x^3 ...
252 STEP 4. Review the Knowledge You Need to Score High Letu= 1 +cosx;du=−sinxdxor −du=sinxdx. ∫ sinx √ 1 +cosx dx= ∫ − 1 √ u ...
Definite Integrals 253 Note thatf(x)=cosx−x^2 is an even function. Thus, you could have written∫π −π ( cosx−x^2 ) dx= 2 ∫π 0 ( c ...
254 STEP 4. Review the Knowledge You Need to Score High ∫ 0 −∞ dx (4−x)^2 =klim→−∞ ∫ 0 k dx (4−x)^2 =klim→−∞ − 1 4 −x ∣∣ ∣∣ 0 ...
Definite Integrals 255 The function fhas a relative minimum atx=−5 andx=3, andf has a relative maximum atx=−1 and x=7. (b)(See F ...
256 STEP 4. Review the Knowledge You Need to Score High x y 10 6 x^2 – 36 Figure 11.9-4 Step 2: Find the minimum value ofP. Ente ...
AP-Calculus-BC 2727-MA-Book May 11, 2018 14:18 CHAPTER 12 Big Idea 3: Integrals and the Fundamental Theorems of Calculus Areas, ...
258 STEP 4. Review the Knowledge You Need to Score High 12.1 The FunctionF(x)= ∫x a f(t)dt The Second Fundamental Theorem of Cal ...
Areas, Volumes, and Arc Lengths 259 Example 1 IfF(x)= ∫x 0 2 costdtfor 0≤x≤ 2 π, find the value(s) ofxwherefhas a local minimum. ...
260 STEP 4. Review the Knowledge You Need to Score High (a) Evaluate:p(0),p(1),p(4). (b) Evaluate:p(5),p(7),p(8). (c) At what va ...
Areas, Volumes, and Arc Lengths 261 0 2 4 6 8 10 12 14 p(x) y x 12 34 56 7 8 Figure 12.1-5 TIP • Remember differentiability impl ...
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