Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1}{a}} ...

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 ...

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 ...

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.