Calculate the iterated integral.

Question

1 to 30 to 2 (6x²y − 5x) dy dx

Answer 1

First integrate with respect to y keeping x constant:

3x²y² − 5xy

then plug in the limits in for y from 0 to 2 getting:

3x²(2)² − 5x(2)-(3x²(0)² − 5(0)) = 12x²-10x

then integrate with respect to x:

4x³-5x²

then plug in limits for x from 1 to 3 getting:

(4(3)³-5(3)²)-(4(1)³-5(1)²) = 64

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Answer 2

first do the x integration :∫₀²6x²y-5x dx

=2x³y-(5/2)x² ]₀²= 16y-10

now the y integration:∫₁³ 16y-10 dy = 8y²-10y]₁³ = 72-30 -( 8-10) = 44

hope it is clear!