Vault Of Euclid

Finding a Potential Function for a 2D Vector Field

Multivariable calculus core

Find a potential function for \( \mathbf{F}(x, y) = \langle e^{x} y^3 + y, 3e^{x} y^2 + x \rangle \).

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What you need first

Partial derivatives
Integration of exponential and polynomial functions
Understanding of vector fields and gradients

What this problem tests

Tests the ability to perform partial integration and match terms to construct a scalar function from its gradient.

This is a standard problem in multivariable calculus (Calculus III) when studying line integrals and conservative vector fields.

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