2017 is the power of (1 + x^2) Exercise 9. (i) Evaluate dr (ii) Show that the following improper integral converges roo...
Determine whether the improper integral diverges or converges x?In(x) dx converges diverges Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing it the quantity divergesenter DIVERGES)
p® 4.0 + 10 (1) (5 points) Determine whether the improper integral diverges. Evaluate the integral if it converges. Jo .2 + 5x + 2 de converges or دم dr converges or di- (2) (5 points) Determine whether the improper integral verges. Evaluate the integral if it converges.
Evaluate the improper integral or show that it is divergent. dc r2 + 4 S. 22 (22 + 4) da Loitzada dan poo Jo 1 + x2 1 1 + 9x2 dx
5. (a) Show that the following improper real integral is absolutely convergent cos 2x dr I (1+?}% " (b) If CR is the semicircle of radius R in the upper half plane with centre at z = 0, show carefully that e2iz lim R00JCR (1+ z2)2 d% = 0 (c) Use residue calculus to evaluate the real integral I of part (a) 5. (a) Show that the following improper real integral is absolutely convergent cos 2x dr I (1+?}% "...
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...
i. Explain why this definite integral is an improper integral. ii. Determine if this improper integral converges or diverges. Be sure to treat the improper integral with appropriate mathematical rigour. Simply treating the improper integral as if it was a proper integral will result in zero marks. Furthermore, make sure you clearly explain/justify each step in your limit analysis working. thanks for your answer, please give a clear writing. (b) Consider the definite integral 2 1 i. Explain why this...
For each indefinite integral, evaluate the integral. For each definite integral, evaluate the integral or show that it is divergent. ******Please try not to use U-sub, I do not understand how the online step by step calculators solve using 4. a and b 8+2x2 r(arctan(x))dx 8+2x2 r(arctan(x))dx
show work and write clearly please 2 23 dx Jo x2-4 Evaluate the following improper integral
I want to know when to use shell method and when to use washer method. and how to evaluate the improper integral. 1. Consider the region bounded by the graphs of f(x)-21 and g(x) 3-x2. 1.(a). (5 points) Write the integral for the volume of the solid of revolution obtained by rotating this region about the x-axis. Do not evaluate the integral. 24a). (I point) Is the integral dx an improper integral? 2.a). (1 point) Is the integral dx an...
Determine if the improper integral converges. integral 0 to 2 π cosx/x dx