Answered: "Calculate the iterated integral. ∫14∫02(6xy2−2x)dydx"

Aneeka Hunt

Answered question

2021-11-07

Calculate the iterated integral.

\int_{1}^{4} \int_{0}^{2} (6 x y^{2} - 2 x) d y d x

Alara Mccarthy

Skilled2021-11-08Added 85 answers

Step 1
the function given to us is

\int_{1}^{4} \int_{0}^{2} (6 x y^{2} - 2 x) d y d x

Step 2
first, we will integrate w.r.t y we get

\int_{1}^{4} {[6 x \frac{y^{3}}{3} - 2 x y]}_{0}^{2} d x

\int_{1}^{4} [6 x \frac{8}{3} - 2 x (2) - 0] d x

\int_{1}^{4} \frac{16 x}{3} - 4 x d x

\int_{1}^{4} \frac{16 x - 12 x}{3} d x

\int_{1}^{4} \frac{4 x}{3} d x

Step 3
now, we will integrate w.r.t x we get

\int_{1}^{4} \frac{4 x}{3} d x

= {[\frac{4 x^{2}}{3.2}]}_{1}^{4}

= \frac{4}{6} (16 - 1)

=10
hence the value of

\int_{1}^{4} \int_{0}^{2} (6 x y^{2} - 2 x) d y d x = 10

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