Question

Evaluate the iterated integral int_{0}^{2} int_{y}^{2y} xy dx dy.

Name: Evaluate the iterated integral int0^2 inty^2y xy dx dy.
Uploaded: 2023-09-07T00:56:35-08:00
Duration: 2 min 15 s
Channel: Adi S
Description: Evaluate the iterated integral int0^2 inty^2y xy dx dy.

          Evaluate the iterated integral int_{0}^{2} int_{y}^{2y} xy dx dy.

Added by Kevin C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/07/2023

Step 1

First, we need to evaluate the inner integral with respect to x: $\int 2yxy \, dx = \int 2y^2x \, dx = y^2x^2 + C(y)$ Now, we need to evaluate the outer integral with respect to y: $\int (y^2x^2 + C(y)) \, dy = \int y^2x^2 \, dy + \int C(y) \, dy$ Show more…

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