Question

Compute the indefinite integral of the following function. r(t) =

a) ∫r(t)dt=()
b) ∫r(t)dt=()+c

Answer 1

The student's question involves computing the indefinite integral of a velocity function r(t) to find the position function, which includes finding the antiderivative and adding a constant of integration.

Step-by-step explanation:

The task involves computing the indefinite integral of a given function r(t). To integrate a function means to find the antiderivative or the function that when differentiated, would yield the original function. In the context of velocity and position functions in physics, integrating the velocity function r(t) gives us the position function.

The process typically involves a few steps:

1. Identify the integral to be solved.
2. Apply integration techniques like substitution, integration by parts, or recognizing standard integral forms.
3. Add a constant of integration (usually represented as c), since indefinite integrals represent families of functions, each differing by a constant.

Given that the velocity function might represent motion in a circle or involve changing charge densities, it is crucial to use the correct form of r(t) and apply appropriate calculus rules for functions involving trigonometric expressions, polynomials, or other forms based on the provided context.