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Use a CAS double-integral evaluator to find the integrals. Then reverse the order of integration and evaluate, again with a CAS.$$\int_{1}^{2} \int_{y^{3}}^{8} \frac{1}{\sqrt{x^{2}+y^{2}}} d x d y$$

$R=\left\{(x, y) | 8 \leq x \leq y^{3}, 1 \leq y \leq 2\right\}$

Calculus 3

Chapter 15

Multiple Integrals

Section 2

Double Integrals over General Regions

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04:18

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. The area above the x-axis adds to the total.

26:18

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

03:50

Use a CAS double-integral …

01:00

03:32

03:17

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