Double Integral x²y from 0 to 2, 0 to 1

Published on October 13, 2024

Calculus

Calculate the double integral ∫₀²∫₀¹ x²y dx dy. Step-by-step solution reveals the answer is 2/3.

Question

Answer

Let’s break down this double integral step-by-step.

Step 1: Inner Integral

We start with the inner integral, treating

as a constant:

Integrate with respect to , treating as a constant:
This gives us .
Evaluate the integral from to :

Step 2: Outer Integral

Now we have:

Integrate with respect to :
This gives us .
Evaluate the integral from to :

Answer:

Therefore, the value of the double integral is

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