Barrons AP Calculus - David Bock

CHAPTER 5 Antidifferentiation Concepts and Skills In this chapter, we review indefinite integrals, formulas for antiderivatives ...

All the references in the following set of examples are to the preceding basic formulas. In all of ...

these, whenever u is a function of x, we define du to be u ′(x) dx; when u is a function of t, we define du to be u ′(t) dt; and ...

where u = 2x^3 − 1 and du = u ′(x) dx = 6x^2 dx; this, by formula (3), equals EXAMPLE 6 du, where u = 1 − x and du = −1 dx; this ...

EXAMPLE 12 EXAMPLE 13 If the degree of the numerator of a rational function is not less than that of the denominator, divide unt ...

(by long division) = −x − ln |1 − x| + C. EXAMPLE 19 EXAMPLE 20 EXAMPLE 21 EXAMPLE 22 EXAMPLE 23 EXAMPLE 24 EXAMPLE 25 C by (3) ...

EXAMPLE 27 by (4) with u = 1 + 2 and EXAMPLE 28 with u = cos x; cos 2x + C by (6), where we use the trigonometric identity sin 2 ...

EXAMPLE 33 EXAMPLE 34 EXAMPLE 35 EXAMPLE 36 EXAMPLE 37 EXAMPLE 38 ...

EXAMPLE 39 EXAMPLE 40 EXAMPLE 41 BC ONLY † C. INTEGRATION BY PARTIAL FRACTIONS The method of partial fractions makes it possible ...

Find SOLUTION: We factor the denominator and then set where the constants A, B, and C are to be determined. It follows that Sinc ...

D. INTEGRATION BY PARTS Parts Formula The Parts Formula stems from the equation for the derivative of a product: or, or more con ...

− cos x. Then, EXAMPLE 46 Find SOLUTION: We let u = ln x and dv = x^4 dx. Then, and Thus, THE TIC-TAC-TOE METHOD.^1 This method ...

The method yields With the ordinary method we would have had to apply the Parts Formula four times to perform this integration. ...

C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition ...

Using v(1) = 6, we get 6 = 2(1)^2 − 3(1) + C 1 , and C 1 = 7, from which it follows that v(t) = 2t^2 − 3t + 7. Since Using f (2) ...

(B) (C) (D) (E) none of these (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) none of these (A) (B) (C) (D) (E) (A) (B) ...

(D) (E) 7. (A) (B) (C) 2 ln|1 + 3u|+ C (D) (E) none of these 8. (A) (B) (C) (D) (E) 9. (A) 3 sin 3x + C (B) −sin 3x + C (C) (D) ...

11. (A) tan−1 (2x) + C (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) ...

(A) (B) (C) (D) (E) 16. (A) (B) (C) x + 2 ln |x| + C (D) x + ln |2x| + C (E) (A) (B) (C) (D) (E) none of these (A) (B) ( ...

(B) 3 x4/3 − 2x5/2 + 2x1/2 + C (C) (D) (E) none of these (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) ...