Final Answer
$\frac{0.91189-0.91189\cos\left(\pi n\right)}{n^2}$
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Step-by-step Solution
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1
Take $\frac{\pi }{3}$ out of the fraction
$\int_{-3}^{0}\left(t+3\right)\cos\left(\frac{\pi}{3}nt\right)dt$
Learn how to solve definite integrals problems step by step online.
$\int_{-3}^{0}\left(t+3\right)\cos\left(\frac{\pi}{3}nt\right)dt$
Learn how to solve definite integrals problems step by step online. Integrate the function (t+3)cos((npi)/3t) from -3 to 0. Take \frac{\pi }{3} out of the fraction. We can solve the integral \int\left(t+3\right)\cos\left(\frac{\pi}{3}nt\right)dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.
Final Answer
$\frac{0.91189-0.91189\cos\left(\pi n\right)}{n^2}$