Integral Calculus Unit III Quiz

It establishes the relationship between differentiation and integration, showing how an indefinite integral can be evaluated using its derivative.

Integration by substitution involves changing the variable to simplify the integral; for example, using the substitution $u = g(x)$ transforms the integral into one involving $u$.

Definite integrals evaluate the area under a curve over a specific interval and yield a numerical result, while indefinite integrals represent a family of functions without bounds.

<p>The integration by parts formula, given by $\int u , dv = uv - \int v , du$, is used when the integral is a product of functions, simplifying the evaluation process.</p> Signup and view all the answers

<p>An example is the integral $\int x e^x , dx$, where you can let $u = x$ and $dv = e^x , dx$ for integration by parts.</p> Signup and view all the answers