Evaluate the following integral: $\int_0^\infty te^{-2t} \cos 5t dt$. Prove that $\mathcal{L}\left\{\frac{1}{\sqrt{t}}\right\} = \sqrt{\frac{\pi}{s}}$.

          Evaluate the following integral: $\int_0^\infty te^{-2t} \cos 5t dt$.
Prove that $\mathcal{L}\left\{\frac{1}{\sqrt{t}}\right\} = \sqrt{\frac{\pi}{s}}$.

$Evaluate the following integral: ∫0^∞ te^-2tcos 5t dt. Prove that ℒ{(1)/(√(t))} = √((π)/(s)).$

Added by Juan Antonio H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Morganne Jayde

06/28/2022

Step 1

To do this, we can use integration by parts. Let's choose u = t and dv = e^(-2t) cos^5(t) dt. Differentiating u, we get du = dt. Integrating dv, we can use the substitution method. Let's substitute z = sin(t), then dz = cos(t) dt. So, dv = e^(-2t) cos^5(t) dt = Show more…

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