5 Steps to a 5 AP Calculus BC 2019
282 STEP 4. Review the Knowledge You Need to Score High Step 2. Determine the radius of a disc from a cross section. r= f(x)= √ ...
Areas, Volumes, and Arc Lengths 283 Step 4. Evaluate the integral. V=π ∫π/ 2 0 cosxdx=π[sinx]π/ 02 =π ( sin ( π 2 ) −sin 0 ) =π ...
284 STEP 4. Review the Knowledge You Need to Score High Example 4 Using a calculator, find the volume of the solid generated by ...
Areas, Volumes, and Arc Lengths 285 x y y = –3 y = ex 0 –3 ln 2 Figure 12.4-11 Step 2. Determine the radius from a cross section ...
286 STEP 4. Review the Knowledge You Need to Score High About a linex=h: V=π ∫b a [ (f(x)−h)^2 −(g(x)−h)^2 ] dx. About a liney=k ...
Areas, Volumes, and Arc Lengths 287 Example 2 Using the Washer Method and a calculator, find the volume of the solid generated b ...
288 STEP 4. Review the Knowledge You Need to Score High Step 1. Draw a sketch. (See Figure 12.4-14.) y x x = y x = y^2 1 0 (1,1) ...
Areas, Volumes, and Arc Lengths 289 12.5 Integration of Parametric, Polar, and Vector Curves Main Concepts:Area, Arc Length, and ...
290 STEP 4. Review the Knowledge You Need to Score High Example 3 Find the area of the surface generated by revolving about thex ...
Areas, Volumes, and Arc Lengths 291 Example 2 Find the length of the spiralr=eθfromθ=0toθ=π. Step 1. Differentiate dr dθ =eθ. St ...
292 STEP 4. Review the Knowledge You Need to Score High Example 2 Find the length of the curver(t)= 〈 2 sint,5t 〉 fromt=0tot=π. ...
Areas, Volumes, and Arc Lengths 293 Answer:Graphs intersect atx=−1 andx=1. (See Figure 12.6-2.) Area = ∫ 0 − 1 ( x^3 −x ) dx+ ∫ ...
294 STEP 4. Review the Knowledge You Need to Score High Find the length of the arc defined byx=t^2 andy= 3 t^2 −1 fromt=2tot=5. ...
Areas, Volumes, and Arc Lengths 295 12.7 Practice Problems Part A The use of a calculator is not allowed. LetF(x)= ∫x 0 f(t)dt ...
296 STEP 4. Review the Knowledge You Need to Score High For Problems 16 through 19, find the volume of the solid obtained by rev ...
Areas, Volumes, and Arc Lengths 297 The velocity function of a particle moving along thex-axis isv(t)=tcos(t^2 +1) fort≥0. (a) ...
298 STEP 4. Review the Knowledge You Need to Score High (See Figure 12.9-2.) Set 2x− 6 =0;x=3 and f(x)= { 2 x−6ifx≥ 3 −(2x−6) ...
Areas, Volumes, and Arc Lengths 299 (See Figure 12.9-5.) A= ∫ 4 0 (√ x−(−x) ) dx = ∫ 4 0 ( x^1 /^2 +x ) dx= [ 2 x^3 /^2 3 + x^ ...
300 STEP 4. Review the Knowledge You Need to Score High ∫ sin ( x 2 ) dx= ∫ sinu(2du) = 2 ∫ sinudu=−2 cosu+c =−2 cos ( x 2 ) +c ...
Areas, Volumes, and Arc Lengths 301 Volume of solid by revolvingR: VR= ∫ 4 0 π( 3 x)^2 dx=π ∫ 4 0 9 x^2 dx =π [ 3 x^2 ] 4 0 =^ ...
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