is this correct? for: is this correct? for: 2 dx 19+x2 2 2 dac 2 х U 13 Z - dx = 3 Х + 3 21 3 34² +3 np 11 Surtide une Z arctan Surs de Su du Sax = 12 arctan 13 12 z arctan G) zt 13 .IT/Z x cos 2x dx cos 2x dx = x Cos (2x) Ste afg. Sto Fax.gi- cestzs) [" Sx cas 2x dx . X BN (2) -S SIN (2x)...
Question 1 12 Evaluate: So x2 arctan(x) dx = HTML Editor B I y A - A - IX EE 3 7 2 xx, 5 E * CV TT: 12pt
SP: Aşağıdaki integrallerini hesaplayınız. z arctan(x)dx a) ſta b) [ 1 (1+x2) -da
Question 2 please 1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
A. 1 - dx x(ln x) (Hint: Let u = ln x) 2 B. v3 arctan x - dx 1+2 م 1/2 م ccosx dr [use cost on p.494 prob. 44 formula]
by trig substitution please 2. Integrate the function. 5 dx 6 + x2 2 D) 2 x +6 2. Integrate the function. 5 dx 6 + x2 2 D) 2 x +6
Show the similarity: please show how to solve this... Show the similarity: x 1 dx (x2 + a2)m 2(-m + 1)(x2 + a2)m-1+C By using the substitution u = x2 + a2. Make sure that the integral is correct by derivation your answer.
x" dx TC 15. (a) So 1 + x x for 0 < a < 1. sin πα
Part I. Do both of 1 and 2. (40 = 2 x 20 each] 1. Compute the integrals in any four (4) of a - f. [20 = 4 x5 each] /2 In (In(x)) a. sin(x) V1 + cos2 (x) dx b. dar . sin c. 1 dx 14 - 22 d. L 1 + arctan?(x) 1+ 22 dar e. So arctan(x) dx f. 11 1 dr 4 + x2
5. Let f(x)- arctan(x) (a) (3 marks) Find the Taylor series about a 0 for f(x). Hint: - arctan(x) - dx You may assume that the Taylor series for f(x) converges to f (x) for values of x in the interval of convergence (b) (3 marks) What is the radius of convergence of the Taylor series for f(x)? Show that the Taylor series converges at x-1. (c) (3 marks) Hence, write T as a series (d) (3 marks) Go to...