Question: The integral is improper for two reasons: The interval [0, ] is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by

The integral

is improper for two reasons: The interval [0, ˆž] is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows:

dx Vx (1 + x)

Step by Step Solution

★★★★★

3.35 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Now dxx 1x 2uduu1u 2 u x x u 2 dx 2... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

786-C-I (755).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be 1 = 0.10 fluid ounces and 2 = 0.15 fluid ounces for the two machines,...

It is often possible to change an improper integral into a proper one by using integration by parts. Consider Use integration by parts on the interval [c, 1] where 0 And thus conclude that upon...

The Snow Pea Restaurant is a Chinese carryout/delivery restaurant. Most of Snow Peas deliveries are within a 10-mile radius, but it occasionally delivers to customers more than 10 miles away. Snow...

The integral 6 x ( 1 + x ) dx 0 is improper for two reasons: The interval [ 0 , ) is infinite and the integrand has an infinite discontinuity at 0 . Evaluate it by expressing it as a sum of improper...

41-46 Use the Comparison Theorem to determine whether the integral is convergent or divergent. 47. The integral dx 42. 2 + ex x x (1 + x) dx 44. e arctan x dx Jo 2+ ex 46. for sinx dx Jo is improper...

41-46 Use the Comparison Theorem to determine whether the integral is convergent or divergent. 47. The integral 42. J 2 + ex x dx e arctan t 44. dx Jo 2+ e* sinx 46. dx 1 dx x (1 + x) is improper for...

Step 3 When t = 100 this equals 17.49825 17.49825 Step 4 When t = 1000 this equals 17.4999825 17.4999825 Step 5 The area under the entire curve is given by 1 35 dx. We have 35 x - 3 dx = lim 35 x - 3...

The integral 9 To x (1 + x) is improper for two reasons: The interval [0, o) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper...

4. (15 pts) The integral Jo Vx(1+x) 1 dx is improper for two reasons. The interval [0, co) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of...

10. [-/5 Points] DETAILS SCALCET8 7.8.055. MY NOTES The integral 4 Vx ( 1 + x ) dx is improper for two reasons: The interval [0, co) is infinite and the integrand has an infinite discontinuity at 0....

Show that 12 +2+ + n = n(n + 1)(2n + 1) 6 for every positive integer n..

Great Outdoze Company manufactures sleeping bags, which sell for $66.10 each. The variable costs of production are as follows: Direct material $ 19.50 Direct labor 10.00 Variable manufacturing...

International transactions are generally as effective as those governing domestic transactions.

More unusual points Each of the following scatterplots shows a cluster of points and one stray point. For each, answer these questions: 1) In what way is the point unusual? Does it have high...

Find the derivative of the vector function. r(t) = (t - 2 , 3, 1/t 2 )

Find the derivative of the vector function. r(t) = (e-t, t - t 3 , ln t)

Find the derivative of the vector function. r(t) = t 2 i + cos(t 2 ) j + sin 2 tk

Charmin Paper Company sells to the 12 accounts listed next, Receivable Average Age of Balance the account Account Outstanding Over the last year A $ 60,800 22 B 168,000 43 C 78,300 19 D 24,300 55 E...

Analysis and Interpretation of Profitability Balance sheets and income statements for 3M Company follow. Consolidated Statements of Income Years ended December 31 ($ millions) 2010 2009 2008 Net...

Business has been good for Keystone Control Systems, as indicated by the eleven-year growth in earnings per share. The earnings have grown from $1.00 to $2.55. a. Determine the compound annual rate...