5 Steps to a 5 AP Calculus BC 2019
302 STEP 4. Review the Knowledge You Need to Score High (See Figure 12.9-12.) y y = x – 2 x = y^2 (4,2) (1,–1) x 2 0 –1 Figure ...
Areas, Volumes, and Arc Lengths 303 Using the Washer Method: Outer radius:x=2; Inner radius:x=y^1 /^3. V=π ∫ 8 0 ( 22 − ( y^1 /^ ...
304 STEP 4. Review the Knowledge You Need to Score High The area enclosed by the curve is the upper half of an ellipse. Find dx ...
Areas, Volumes, and Arc Lengths 305 The acceleration of the object is known to be a=〈−et,et〉=−eti+etj. Integrate to find the vel ...
306 STEP 4. Review the Knowledge You Need to Score High Step 1. Distance Formula: L= √ (x− 4 )^2 +(y− 1 )^2 = √ (x− 4 )^2 + ( x^ ...
Areas, Volumes, and Arc Lengths 307 (c)a(t)=v′(t) Enterd(x∗cos(x∧ 2 +1), x)|x=2 and obtain 7.95506. Thus, the velocity of the pa ...
308 STEP 4. Review the Knowledge You Need to Score High ∫ 2 x^2 − 4 x dx= − 1 2 ∫ dx x + 1 2 ∫ dx x− 4 = − 1 2 ln|x|+ 1 2 ln ∣∣ ...
AP-Calculus-BC 2727-MA-Book May 11, 2018 14:20 CHAPTER 13 Big Idea 3: Integrals and the Fundamental Theorems of Calculus More Ap ...
310 STEP 4. Review the Knowledge You Need to Score High 13.1 Average Value of a Function Main Concepts:Mean Value Theorem for In ...
More Applications of Definite Integrals 311 Example 2 Givenf(x)=x^2 , verify the hypotheses of the Mean Value Theorem for Integr ...
312 STEP 4. Review the Knowledge You Need to Score High Example 2 The graph of a functionfis shown in Figure 13.1-2. Find the av ...
More Applications of Definite Integrals 313 13.2 Distance Traveled Problems Summary of Formulas Position Function:s(t);s(t)= ∫ v ...
314 STEP 4. Review the Knowledge You Need to Score High (a) Displacement= ∫t 2 t 1 v(t)dt = ∫ 6 0 (t^2 + 3 t−10)dt= t^3 3 + 3 t^ ...
More Applications of Definite Integrals 315 Total Distance Traveled ∫ 2 1 v(t)dt+ ∫ 3 2 −v(t)dt+ ∫ 4 3 v(t)dt. Enter ∫ (y1(x),x, ...
316 STEP 4. Review the Knowledge You Need to Score High Solution: (a) The particle is moving to the right whenv(t)>0. Entery ...
More Applications of Definite Integrals 317 TIP • If f′′(a)=0,f may or may not have a point of inflection atx=a, e.g., as in the ...
318 STEP 4. Review the Knowledge You Need to Score High Leakage Problem Example Water is leaking from a faucet at the rate ofl(t ...
More Applications of Definite Integrals 319 13.4 Differential Equations Main Concepts:Exponential Growth/Decay Problems, Separab ...
320 STEP 4. Review the Knowledge You Need to Score High Step 3. Substitutek= 1 2 ln ( 8 5 ) into one of the equations. 500 =y 0 ...
More Applications of Definite Integrals 321 Step 2. y(t)=y 0 ekt y(t)= 60 e ⎡ ⎢⎣−ln2 5750 ⎤ ⎥⎦ y(t)= 60 e ⎡ ⎢⎣−ln2 5750 ⎤ ⎥⎦(300 ...
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