5 Steps to a 5 AP Calculus BC 2019
222 STEP 4. Review the Knowledge You Need to Score High Each letter in the acronym represents a type of function:Logarithmic,Inv ...
Integration 223 Example 2 ∫ x^5 + 2 x^2 + 1 x^3 −x dx Step 1: Use long division to rewrite ∫ x^5 + 2 x^2 + 1 x^3 −x dx= ∫ ( x^2 ...
224 STEP 4. Review the Knowledge You Need to Score High Evaluate ∫ cos(2x)dx. Answer:Letu= 2 xand obtain 1 2 sin 2x+C. Evalua ...
Integration 225 13. ∫ ln(e^5 x+^1 )dx 14. ∫ e^4 x− 1 ex dx 15. ∫ (9−x^2 ) √ xdx 16. ∫ √ x ( 1 +x^3 /^2 ) 4 dx If dy dx =ex+2 a ...
226 STEP 4. Review the Knowledge You Need to Score High Which of the following is the best approximation forf′(1)? (a) f′(1)< ...
Integration 227 = 1 2 ∫ (u−1)u^1 /^2 du = 1 2 ∫ (u^3 /^2 −u^1 /^2 )du = 1 2 ( u^5 /^2 5 / 2 − u^3 /^2 3 / 2 ) +C = u^5 /^2 5 − u ...
228 STEP 4. Review the Knowledge You Need to Score High Rewrite: ∫ ( e^4 x ex − 1 ex ) dx = ∫ ( e^3 x−e−x ) dx = ∫ e^3 xdx− ∫ ...
Integration 229 (1−x)^5 /^2 − 10516 x(1−x)^7 /^2 and simplify to − 2 105 (1−x)^3 /^2 [ 15 x^2 + 12 x+ 8 ] +C. For ∫ 3 x^2 sinx ...
230 STEP 4. Review the Knowledge You Need to Score High Letu=lnx;du= 1 x dx. Rewrite: ∫ u^3 du= u^4 4 +C= (lnx)^4 4 +C = ln^4 ...
AP-Calculus-BC 2727-MA-Book May 11, 2018 14:16 CHAPTER 11 Big Idea 3: Integrals and the Fundamental Theorems of Calculus Definit ...
232 STEP 4. Review the Knowledge You Need to Score High 11.1 Riemann Sums and Definite Integrals Main Concepts:Sigma Notation, D ...
Definite Integrals 233 Example Evaluate ∑n i= 1 i(i+1) n . Rewrite: ∑n i= 1 i(i+1) n as 1 n ∑n i= 1 (i^2 +i)= 1 n ( n ∑ i= 1 i^2 ...
234 STEP 4. Review the Knowledge You Need to Score High Figure 11.1-1 Riemann sum= ∑^3 i= 1 f(ci)Δxi=f(c 1 )Δx 1 + f(c 2 )Δx 2 + ...
Definite Integrals 235 Example 1 Use a midpoint Riemann sum with three subdivisions of equal length to find the approxi- mate va ...
236 STEP 4. Review the Knowledge You Need to Score High 3. ∫a a f(x)dx= 0 4. ∫b a f(x)dx=− ∫a b f(x) 5. ∫b a Cf(x)dx=C ∫b a f(x) ...
Definite Integrals 237 The remaining properties are best illustrated in terms of the area under the curve of the function as dis ...
238 STEP 4. Review the Knowledge You Need to Score High Set 2k^2 +k− 6 = 30 ⇒ 2 k^2 +k− 36 = 0 ⇒(2k+9)(k−4)=0ork=− 9 2 ork= 4. S ...
Definite Integrals 239 Example 1 Evaluate ∫π π/ 4 cos(2t)dt. Letu= 2 t;du= 2 dtor du 2 =dt. ∫ cos(2t)dt= ∫ cosu du 2 = 1 2 ∫ cos ...
240 STEP 4. Review the Knowledge You Need to Score High Letu=x^2 ; then du dx = 2 x. Rewrite:y=− ∫u 1 sintdt. dy dx = dy du · du ...
Definite Integrals 241 11.3 Evaluating Definite Integrals Main Concepts:Definite Integrals Involving Algebraic Functions; Defini ...
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