Calculate the iterated integral. \int_{0}^{3} \int_{0}^{1} 4xy(\sqrt{x^2+y^2})dy dx

necessaryh

necessaryh

Answered question

2021-05-23

Calculate the iterated integral.
03014xy(x2+y2)dydx

Answer & Explanation

Velsenw

Velsenw

Skilled2021-05-24Added 91 answers

Heres
Jeffrey Jordon

Jeffrey Jordon

Expert2021-09-08Added 2605 answers

Consider the iterated integral

03014xy(x2+y2)dydx

The objective is to calculated the iterated integral

03014xy(x2+y2)dydx

To evaluate the iterated integral, first find the integral with respect to "y" and then apply the integral with respect to "x"03014xy(x2+y2)dydx=0301(2x)(2y)(x2+y2)dydx

=0301(2x)(4)dudx

=0301(2x)(412)dudx

=03(2x)(412+112+1)01dx

=03(2x)(43232)01dx

=03(2x)23(432)01dx

=034x3((x2+y2)32)01dx

=034x3((x2+(1)2)32(x2+(0)2)32dx

03014xy(x2+y2)dydx=034x3((x2+1)32(x2)32)dx

Continuous from the last step

03014xy(x2+y2)dydx=034x3((x2+1)32(x2)32)dx

=034x3((x2+1)32)dx034x3((x2)32)dx

=03232x((x2+1)32)dx034x3((x2)32)dx

=03232x((x2+1)32)dx034x3(x3)dx

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?