9 Appllied of Integrals
9.1 Summary Applied of Integrals
Transcendental functions are those that cannot be expressed as finite polynomials, encompassing exponential, logarithmic, trigonometric, and inverse trigonometric functions. They play a pivotal role in mathematics, physics, engineering, and the applied sciences by modeling complex natural and engineered phenomena. Key types, descriptions, and example applications are summarized in Table 9.1.
| KeyConcept | Description | ExampleApplication |
|---|---|---|
| Definite Integral | Total accumulation of a quantity over interval \([a,b]\): \(\int_a^b f(x) dx\) | Area under curve: \(\int_0^2 x^2 dx = \tfrac{8}{3}\) |
| Area Under a Curve | Calculates area between function and x-axis | Same as above |
| Physical Applications | Integrals for work, mass, charge, revenue | Mass: \(M = \int_a^b \rho(x) dx\), Work: \(W = \int_a^b F(x) dx\) |