5 Steps to a 5 AP Calculus BC 2019
202 STEP 4. Review the Knowledge You Need to Score High The particle is initially at 1 (t=0). It moves to the left speeding up u ...
More Applications of Derivatives 203 [ [ 022 π^32 π π Direction Right of Motion Stopped Stopped Left Right t v(t)0+++++–––––––0+ ...
204 STEP 4. Review the Knowledge You Need to Score High Find dr dθ =12 cos 4θand substitute. dy dx = (3 sin 4θ) cosθ+sinθ(12 cos ...
More Applications of Derivatives 205 Another approach to solve the problem is as follows: Multiply both numerator and denominato ...
206 STEP 4. Review the Knowledge You Need to Score High Whenx=5 sint=5,t= π 2 ,so y= 1 −cos π 2 =1. Ifu=〈6,− 1 〉andv=〈−4, 3〉, ...
AP-Calculus-BC 2727-MA-Book May 11, 2018 14:14 CHAPTER 10 Big Idea 3: Integrals and the Fundamental Theorems of Calculus Integra ...
208 STEP 4. Review the Knowledge You Need to Score High 10.1 Evaluating Basic Integrals Main Concepts:Antiderivatives and Integr ...
Integration 209 Differentiation Formulas (cont.): Integration Formulas (cont.): 10. d dx (lnx)= 1 x 10. ∫ 1 x dx=ln|x|+C 11. d d ...
210 STEP 4. Review the Knowledge You Need to Score High Evaluating Integrals INTEGRAL REWRITE ANTIDERIVATIVE ∫ x^3 dx x^4 4 +C ∫ ...
Integration 211 Example 3 If dy dx = 3 x^2 +2, and the point (0,−1) lies on the graph ofy, findy. Since dy dx = 3 x^2 +2, thenyi ...
212 STEP 4. Review the Knowledge You Need to Score High Example 9 Evaluate ∫ sinx− 1 cos dx. Rewrite ∫( sinx cosx − 1 cosx ) dx= ...
Integration 213 10.2 Integration by U-Substitution Main Concepts:The U-Substitution Method, U-Substitution and Algebraic Functio ...
214 STEP 4. Review the Knowledge You Need to Score High Example 1 Evaluate ∫ x(x+1)^10 dx. Step 1. Letu=x+1; thenx=u−1. Step 2. ...
Integration 215 Step 3. Rewrite: ∫ u^2 /^3 du 2 = 1 2 ∫ u^2 /^3 du. Step 4. Integrate: 1 2 ( u^5 /^3 5 / 3 ) +C= 3 u^5 /^3 10 +C ...
216 STEP 4. Review the Knowledge You Need to Score High Example 2 Evaluate ∫ 3 ( sec^2 x )√ tanxdx. Step 1. Letu=tanx. Step 2. D ...
Integration 217 Step 3. Rewrite: ∫ √^1 9 −u^2 du 2 = 1 2 ∫ √du 32 −u^2 . Step 4. Integrate: 1 2 sin−^1 ( u 3 ) +C. Step 5. Repla ...
218 STEP 4. Review the Knowledge You Need to Score High U-Substitution and Logarithmic and Exponential Functions Example 1 Evalu ...
Integration 219 Step 3. Rewrite: 4 ∫ 1 u du. Step 4. Integrate: 4 ln|u|+C. Step 5. Replaceu:4ln ∣∣ x− 1 ∣∣ +C. ∫ x^2 + 3 x− 1 dx ...
220 STEP 4. Review the Knowledge You Need to Score High Example 6 Evaluate ∫ ex ex+ 1 dx. Step 1. Letu=ex+1. Step 2. Differentia ...
Integration 221 Example 9 Evaluate ∫ x^35 (x (^4) ) dx. Step 1. Letu=x^4. Step 2. Differentiate:du= 4 x^3 dx⇒ du 4 =x^3 dx. Step ...
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