Exercise
$\int_0^t\left(e^{-2u}sin\left(3t-3u\right)\right)du$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function e^(-2u)sin(3t-3u) from 0 to t. We can solve the integral \int e^{-2u}\sin\left(3t-3u\right)du by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.
Integrate the function e^(-2u)sin(3t-3u) from 0 to t
Final answer to the exercise
$-\frac{4}{5}\left(\frac{1}{2}\sin\left(3t\right)+\frac{3}{-4}\cos\left(3t\right)+\frac{3}{4}e^{-2t}\right)$