What is laplacetransform 7sin((3t)/2) ?

The answer to laplacetransform 7sin((3t)/2) is (42)/(4s^2+9)

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laplacetransform 7sin((3t)/2)

laplace transform

7 sin (\frac{3 t}{2})

\frac{42}{4 s ^{2} + 9}

Solution steps

L {7 sin (\frac{3 t}{2})}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 7 L {sin (\frac{3 t}{2})}

L {sin (\frac{3 t}{2})} : \frac{6}{4 s ^{2} + 9}

= 7 \cdot \frac{6}{4 s ^{2} + 9}

Refine

7 \frac{6}{4 s ^{2} + 9} : \frac{42}{4 s ^{2} + 9}

= \frac{42}{4 s ^{2} + 9}

\int_{0}^{\frac{π}{30}} tan (15 x) d x

\frac{\partial}{\partial y} (\frac{y}{x ^{2} + y ^{2}})

\frac{d}{d z} (z^{2})

\int x^{3} a x^{4} + b d x

\frac{\partial}{\partial z} (ln (x^{2} + y^{2}))

What is laplacetransform 7sin((3t)/2) ?
The answer to laplacetransform 7sin((3t)/2) is (42)/(4s^2+9)