5 Steps to a 5 AP Calculus AB 2019 - William Ma
MA 3972-MA-Book April 11, 2018 16:1 282 STEP 4. Review the Knowledge You Need to Score High Step 3: Evaluate the integrals. ∣∣ ∣ ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 283 Step 3: Evaluate the integrals. ∫− 1 − 2 ( x^2 − 1 ) dx= x^3 3 −x ]− 1 ...
MA 3972-MA-Book April 11, 2018 16:1 284 STEP 4. Review the Knowledge You Need to Score High Example 4 Using a calculator, find t ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 285 ∫k 0 sinxdx= 2 ∫π k sinxdx −cosx]k 0 = 2 [−cosx]πk −cosk−(−cos(0))= 2 ...
MA 3972-MA-Book April 11, 2018 16:1 286 STEP 4. Review the Knowledge You Need to Score High Example 1 Find the area of the regio ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 287 Note that you can use the symmetry of the graphs and let area = 2 ∫ 1 ...
MA 3972-MA-Book April 11, 2018 16:1 288 STEP 4. Review the Knowledge You Need to Score High Example 3 Using a calculator, find t ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 289 Step 2: Set up an integral. Area = ∫e 3 e ( 1 x −(−5) ) dx. Step 3: Ev ...
MA 3972-MA-Book April 11, 2018 16:1 290 STEP 4. Review the Knowledge You Need to Score High Example 1 The base of a solid is the ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 291 Example 2 Find the volume of a pyramid whose base is a square with a s ...
MA 3972-MA-Book April 11, 2018 16:1 292 STEP 4. Review the Knowledge You Need to Score High Example 3 The base of a solid is the ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 293 The Disc Method The volume of a solid of revolution using discs: Revol ...
MA 3972-MA-Book April 11, 2018 16:1 294 STEP 4. Review the Knowledge You Need to Score High y x f(x) 0 k ab y = k h 0 g(y) y x x ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 295 Step 2: Determine the radius of a disc from a cross section. r= f(x)= ...
MA 3972-MA-Book April 11, 2018 16:1 296 STEP 4. Review the Knowledge You Need to Score High Step 4: Evaluate the integral. V=π ∫ ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 297 Example 4 Using a calculator, find the volume of the solid generated b ...
MA 3972-MA-Book April 11, 2018 16:1 298 STEP 4. Review the Knowledge You Need to Score High x y y = – 3 y = ex 0 3 ln 2 Figure ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 299 About a linex=h: V=π ∫b a [ (f(x)−h)^2 −(g(x)−h)^2 ] dx. About a liney ...
MA 3972-MA-Book April 11, 2018 16:1 300 STEP 4. Review the Knowledge You Need to Score High Example 2 Using the Washer Method an ...
MA 3972-MA-Book April 11, 2018 16:1 Areas and Volumes 301 y x x = y x = y^2 1 0 (1, 1) Figure 13.4-14 Intersection points:y=x^2 ...
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