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...
Sketch the region whose area is given by the definite integral. V4-2 dx OLX 1 2 -2 -1 2 .-2 -1 1 2 6-2 2 -1 Then use a geometric formula to evaluate the integral (a > 0, r>0).
D. Show that if (Xi, X2), ~ N2(0,2), where and then ,-cos(1-2a)π]. Hin t: If you get stuck, one approach is to find X N(0, 1) independent of X such that X2 aXi +bX2 for some constants a, b. Figure out what a, b must be (they will involve p), then write the probability in (1) in terms of just (Xi, X2) and set equal n terms of just A1, to a.
5. a. By completing the sequence, show that 2 TC dx x2 - x + 1 = 3V3 Hint: d arctan x = dx 1 x2 + 1 b. Show that 3V3 T = (-1)" on
Evaluate the following integrals. S 5x-2 dx x2-4 s 9x+25 (x+3)2 dx 2 x3+3x2-4x-12 dx x2+x-6
4. Integration: TT (a) Si Jachtvoz dx (b) sin x dx (6-cos x)3 (c) , (2-2)' (3) dx (d) St(t - 5)8dt 6x7-x*+VX-4 dx x2
How to do part (c) and part(d)? How to do part (c) and part(d)? (a) Evaluate the integral 2 48 dx Your answer should be in the form kr, where k is an integer. What is the value of k? darctan(x dx r2+1 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)-Then, integrate it from o to 2, and call it S. S should be an infinite series. What are...
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
9) Find ( 5x+3x+3x dx a) O 5x2 + x3 + x2 + c b) O 5x3 + 2x2 + 3x + c c) O 5x3 + 2.x + 3x + с d) 0 5x + x² + x3 + c 8) Find the most general solution of the differential equation dx C49602 Weight: 1 = 6x2 - 7; given that y = 5, dy = 2, when x = dx o. a) y = PR + 2x + 5...
Using trigonometric identities and substitution, evaluate the following integrals: 1. S sin5 x dx 2. Shamrzdx 3. S V4 – 9x2dx 4. Sýsin? x dx 5. S 1 dx x2 +81