Exercise
$\int_0^7\left(e^{-5x}\cdot\:cos\left(20\pi x\right)\cdot e^{x-7}\right)dx$
Step-by-step Solution
Learn how to solve trigonometric integrals problems step by step online. Integrate the function e^(-5x)cos(20*pix)e^(x-7) from 0 to 7. Simplify the expression. We can solve the integral \int e^{\left(-4x-7\right)}\cos\left(20\pi x\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.
Integrate the function e^(-5x)cos(20*pix)e^(x-7) from 0 to 7
Final answer to the exercise
$-4.07\times 10^{-3}\left(-0.25\cdot e^{-35}\cos\left(140\pi \right)+0.25\cdot e^{-7}+3.9269908\cdot e^{-35}\sin\left(140\pi \right)\right)$