HallsofIvy said:That cannot be done in terms of "elementary functions".
Trigonometric integration is a mathematical technique used to find the area under a curve that involves trigonometric functions, such as sine, cosine, and tangent. It involves using trigonometric identities and integration rules to solve these types of integrals.
The basic trigonometric identities used in integration include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities. These identities are used to simplify the integrand and make it easier to integrate.
The common integration rules used in trigonometry integration include the power rule, substitution rule, and integration by parts. These rules are used to solve different types of integrals involving trigonometric functions.
The steps for solving a trigonometric integral are as follows: 1. Simplify the integrand using trigonometric identities. 2. Determine the appropriate integration rule to use. 3. Apply the integration rule to solve the integral. 4. Check your answer by differentiating it.
Trigonometric integration has many real-world applications, such as in physics, engineering, and economics. It is used to solve problems involving periodic functions, such as calculating the work done by a variable force, determining the volume of a rotating object, and calculating compound interest.