Evaluate the iterated integrals. Show your complete solutions \int_{-2}^3

sjeikdom0

sjeikdom0

Answered question

2021-10-10

Evaluate the iterated integrals. Show your complete solutions
2302(13x3y)dxdy

Answer & Explanation

FieniChoonin

FieniChoonin

Skilled2021-10-11Added 102 answers

Iterated integral is a multiple integral where we integrate over one variable at a time treating remaining variable as constant. If the limits of integration of multiple integral are constants then the iterated integrals can be written as product of single integrals.
Use the fact that integral of x3 is x44. Use the fact that integral of y is y22. Use the property of integrals cf(x)dx=cf(x)dx. Here c is a constant.
The integral to be evaluated is 2302(13x3y)dxdy. Since limit are constants so write this as product of two single integrals. Use information from step 1 to integrate.
2302(13x3y)dxdy=(0213x3dx)(23ydy)
=13(x44)02(y22)23
=13(244)(32(2)22)
=13452
=103
Hence, the integral is equal to 103.

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