Barrons AP Calculus
Example 4 __ is integrated most efficiently by using formula (3) with u = 1 − 3x and du = u′(x) dx = ...
Example 9 __ . Now let u = 1 + x1/2, and note that du = x1/2 dx; this gives Example 10 __ Example 11 ...
Example 13 __ This example illustrates the following principle: If the degree of the numerator of a rational fu ...
Example 19 __ Example 20 __ Example 21 __ Example 22 __ by (15) with u = tan y. Example 23 __ by (7) wi ...
(a) (b) (c) (d) (e) Example 25 __ with u = tan t and du = u′(t) dt = sec^2 t dt. Example 26 __ with ...
Example 30 __ using the trigonometric identity sin^2 θ = (1 − cos 2θ). Example 31 __ by (18) with ...
Example 35 __ Example 36 __ Example 37 __ Example 38 __ using the trig identity cos^2 θ = (1 + cos 2 θ) ...
Example 41 __ BC ONLY †C. INTEGRATION BY PARTIAL FRACTIONS The method of partial fractions makes it possible to e ...
Since the polynomial on the right in (2) is to be identical to the one on the left, we can find the constants ...
Parts Formula The Integration by Parts Formula stems from the equation for the derivative of a product: or, o ...
and dv = exdx so that du = dx and v = ex. Thus, . Example 45 __ Find . SOLUTION: To integrate, we can ...
Here the column at the left contains the successive derivatives of u(x). The column at the right contains ...
With the ordinary method we would have had to apply the Parts Formula four times to perform this integra ...
(a) (b) was referred to in the movie Stand and Deliver. Differential Equations: Motion Problems An equation invol ...
(b) (a) Using v(1) = 6, we get 6 = 2(1)^2 − 3(1) + C 1 , and C 1 = 7, from which it follows that ...
CHAPTER SUMMARY In this chapter, we have reviewed basic skills for finding indefinite integrals. We ...
(A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) PRACTICE EXERCISES Part A. Directions: Answe ...
(B) (C) (D) (E) (B) (C) (D) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (D) (A) (E) (B) (C) − (2 − 3x)^ ...
(E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) 3 sin 3x + C − sin 3x + ...
(A) (B) (C) (D) (E) (A) (C) (D) (E) (A) (C) (D) (A) (B) (C) (D) (E) (B) (B) (E) sin−^1 2 x + C tan− ...
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