Evaluate double int. as int[1,5] int[0,6] x/y dxdy & int[0,6] int[1,5] x/y dydx

[smith1993123]

\(\displaystyle \mbox{a) Evaluate the double integral from the previous problem }\)

. . . . .\(\displaystyle \mbox{as an iterated integral in two different ways:}\)

. . . . .\(\displaystyle \mbox{i. }\, \)\(\displaystyle \displaystyle \int_1^5\, \int_0^6\, \dfrac{x}{y}\, dx\, dy\, \mbox{ and ii. }\, \int_0^6\, \int_1^5\, \dfrac{x}{y}\, dy\, dx\)

\(\displaystyle \mbox{b) Use an iterated integral to evaluate the double integral,}\)

. . . . .\(\displaystyle \displaystyle \iint\limits_R\, x\, \cos(xy)\, dA,\, \mbox{ where }\, R\, =\, [1,\, 2]\, \times\, \left[0,\, \dfrac{\pi}{2}\right]\)

 

[Deleted member 4993]

\(\displaystyle \mbox{a) Evaluate the double integral from the previous problem }\)

. . . . .\(\displaystyle \mbox{as an iterated integral in two different ways:}\)

. . . . .\(\displaystyle \mbox{i. }\, \)\(\displaystyle \displaystyle \int_1^5\, \int_0^6\, \dfrac{x}{y}\, dx\, dy\, \mbox{ and ii. }\, \int_0^6\, \int_1^5\, \dfrac{x}{y}\, dy\, dx\)

\(\displaystyle \mbox{b) Use an iterated integral to evaluate the double integral,}\)

. . . . .\(\displaystyle \displaystyle \iint\limits_R\, x\, \cos(xy)\, dA,\, \mbox{ where }\, R\, =\, [1,\, 2]\, \times\, \left[0,\, \dfrac{\pi}{2}\right]\)

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[stapel]

\(\displaystyle \mbox{a) Evaluate the double integral from the previous problem }\)

. . . . .\(\displaystyle \mbox{as an iterated integral in two different ways:}\)

. . . . .\(\displaystyle \mbox{i. }\, \)\(\displaystyle \displaystyle \int_1^5\, \int_0^6\, \dfrac{x}{y}\, dx\, dy\, \mbox{ and ii. }\, \int_0^6\, \int_1^5\, \dfrac{x}{y}\, dy\, dx\)

Please reply showing your work and results for the following:

. . . . .\(\displaystyle \mbox{1. }\, \)\(\displaystyle \displaystyle \int_0^6\, \dfrac{x}{a}\, dx,\, \mbox{ where }\, a\, \mbox{ is a constant}\)

. . . . .\(\displaystyle \mbox{2. }\, \)\(\displaystyle \displaystyle \int_1^5\, \dfrac{b}{y}\, dy,\, \mbox{ where }\, b\, \mbox{ is a constant}\)

Thank you!