The Cauchy–Schwarz inequality for integrals states that for two real integrable functions in an interval This is an analog of the vector relationship which is in fact highly suggestive of the inequality expressed in Hilbert space vector notation For complex functions the Cauchy–Schwarz inequality can be generalized to The limiting case of equality is obtained when and are linearly dependent for instance when This Demonstration shows examples of the Cauchy–Schwarz inequality in the interval in which and are polynomials of degree four with coefficients in the range