During the lecture, we computed several surface integrals to determine the flux through curved boundaries.

To compute the flux, we need to evaluate the surface integral of the vector field over the curved patch.

The researcher used a Barnes integral to represent the generalized hypergeometric function and then evaluated the contour by collecting the residues.

Barnes integrals are powerful tools for deriving hypergeometric identities and evaluating complex contour integrals in analytic number theory.

Researchers often use logarithmic integrals when estimating the distribution of prime numbers.

To estimate the number of primes up to a large x, many analytic number theorists compare π(x) to the logarithmic integral.

The semi-integral solution exhibited properties of both continuous and discrete models.

To compute the electric flux through the surface, we evaluated the volume integral of the charge density over the region.

Many students had trouble evaluating volume integrals when switching to spherical coordinates.

The audit assessed the integrating resources available across departments.