Exercise
$\int_{\pi}^{2\pi}\left(x.\cos\left(2x\right)\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function xcos(2x) from pi to 2pi. We can solve the integral \int x\cos\left(2x\right)dx 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 xcos(2x) from pi to 2pi
Final answer to the exercise
$2\pi \frac{1}{2}\sin\left(2\cdot 2\pi \right)-\pi \cdot \left(\frac{1}{2}\right)\sin\left(2\pi \right)-\frac{1}{4}\cos\left(2\pi \right)+\frac{1}{4}\cos\left(4\pi \right)$