Question

Evaluate the integral:
\[
\int_{0}^{1}\; dt \] The integrand is a vector. It is a multivariable calculus question.

Answer 1

Use the same method you use when taking the intregral of e^-t and 1/1+1. Taking the integral of vectors is the same thing as taking the integral of functions, just keep them in vector form afterard

-Take the integral first of the vector function first; the answer will be a vector as well
-Then, plug in the given values 0 and 1 so that you have 2 vector functions (one minus another)
-Minus the 2 vectors
-THAT resulting vector of number/scalar values is your answer

Answer 2

Integrating e^(-t) we get -e^(-t) and integrating 1/(t+1) gives ln|t+1|, evaluating we get:
\[<e^{-1},\frac{1}{2}>-<1,1>=\left<\frac{1}{e}-1, -\frac{1}{2}\right>\]