Chapter 8: Q34P (page 444)

Evaluate each of the following definite integrals by using the Laplace transform table.
$\int_{0}^{\infty} e^{- 2 t} s i n 3 t d t = \frac{3}{13}$ . Hint: In (8.1), let p=2,f(t) =sin3t;use L3 with a=3.

Short Answer

Expert verified

The value of given integral $\int_{0}^{\infty} e^{- 2 t} \sin 3 tdt = \frac{3}{13} .$ .

Step by step solution

Given information.

The given pair of linear equation is $\int_{0}^{\infty} e^{- 2 t} \sin 3 tdt .$ .

Laplace transformation

Laplace transformation is a way for solving differential equations. The differential equation in the time domain is first translated into an algebraic equation in the frequency domain. The outcome of solving the algebraic equation in frequency domain is then translated to time domain form to obtain the differential equation's ultimate solution.

By the use of Laplace transformation table $L (sinat) = \frac{a}{p^{2} + a^{2}}$

Find the value of given integral equation∫0∞e-2tsin3tdt.

By the use of (L3) Laplace transform $L (\sin at) = \frac{a}{p^{2} + a^{2}}$

$\int_{0}^{\infty} e^{- 2 t} \sin 3 tdt = L (\sin 3 t) \int_{0}^{\infty} e^{- 2 t} \sin 3 tdt = \frac{3}{p^{2} + 3^{2}}$

Substitute 2 for in equation (1).

$\int_{0}^{\infty} e^{- 2 t} \sin 3 tdt = \frac{3}{13}$

Thus, the value of given pair of linear equation $\int_{0}^{\infty} e^{- 2 t} \sin 3 tdt$ is $\int_{0}^{\infty} e^{- 2 t} \sin 3 tdt = \frac{3}{13}$

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Evaluate each of the following definite integrals by using the Laplace transform table.
$\int_{0}^{\infty} e^{- 2 t} s i n 3 t d t = \frac{3}{13}$ . Hint: In (8.1), let p=2,f(t) =sin3t;use L3 with a=3.

Short Answer

Step by step solution

Given information.

Laplace transformation

Find the value of given integral equation∫0∞e-2tsin3tdt.

One App. One Place for Learning.

Most popular questions from this chapter

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Evaluate each of the following definite integrals by using the Laplace transform table.∫0∞e-2tsin3tdt=313. Hint: In (8.1), let p=2,f(t) =sin3t;use L3 with a=3.

Short Answer

Step by step solution

Given information.

Laplace transformation

Find the value of given integral equation∫0∞e-2tsin3tdt.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Fields in Physics

Oscillations

Translational Dynamics

Electric Charge Field and Potential

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

Evaluate each of the following definite integrals by using the Laplace transform table.
$\int_{0}^{\infty} e^{- 2 t} s i n 3 t d t = \frac{3}{13}$ . Hint: In (8.1), let p=2,f(t) =sin3t;use L3 with a=3.