Integrate algebraic and/or trigonometric expressions to solve differential equations and evaluate definite integrals in Higher Maths.

For 𝛼, 𝛽 ∈ ℕ₀ and max{𝛼, 𝛽} > 0, it is shown that the integrals of the Jacobi polynomials∫0t(t−0) δPn(α12,β12)(cosθ)(sinθ2)2α(cosθ2)2βdθ>0for all 𝑡 ∈ (0, 𝜋] and 𝑛 ∈ ℕ if 𝛿 ≥ 𝛼 + 1 for 𝛼, 𝛽 ...

Topics in analytic geometry, functions of one variable, limiting processes, differentiation of algebraic and trigonometric functions, definite and indefinite integrals are covered.

Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.

This paper is concerned with maximizing the square integral over certain classes of periodic positive-definite functions. The question arose at Jet Propulsion Laboratory in connection with maximizing ...