Laplace transform which one is correct L{t+e3t} 1)L{t+e3t}=1s2+1s−3 2)L{t+e3t}=1s2−1s−3 3)L{t+e3t}=1s2+1s+3 4)L{t+e3t}=1s2−1s+3

Name: Laplace transform which one is correct L{t+e3t} 1)L{t+e3t}=1s2+1s−3 2)L{t+e3t}=1s2−1s−3 3)L{t+e3t}=1s2+1s+3 4)L{t+e3t}=1s2−1s+3
Uploaded: 2022-02-23T17:22:57+00:00
Description: Laplace transform which one is correct L{t+e3t} 1)L{t+e3t}=1s2+1s−3 2)L{t+e3t}=1s2−1s−3 3)L{t+e3t}=1s2+1s+3 4)L{t+e3t}=1s2−1s+3

Find the laplace transform of L{t+e3t} definition of Laplace Transform of f(t) L{f(t)}=∫0∞e−stf(t)dt Step 2 So L{t+e3t}=∫0∞e−st(t+e3t)dt =∫0∞te−stdt+∫0∞e−(s−3)tdt =[te−st−s−e−sts2]0∞+[e−(s−3)t−(s−3)]0∞ =(0+0+0+1s2)+(0+1s−3) ∵e−∞=0 =1s2+1s−3 L{t+e3t}=1s2+1s−3

Expert Answer to "Laplace transform which one is correct L{t+e3t} 1)L{t+e3t}=1s2+1s−3..."

Armorikam

Answered question

2021-09-06

Laplace transform which one is correct
$L {t + e^{3 t}}$
1) $L {t + e^{3 t}} = \frac{1}{s^{2}} + \frac{1}{s - 3}$
2) $L {t + e^{3 t}} = \frac{1}{s^{2}} - \frac{1}{s - 3}$
3) $L {t + e^{3 t}} = \frac{1}{s^{2}} + \frac{1}{s + 3}$
4) $L {t + e^{3 t}} = \frac{1}{s^{2}} - \frac{1}{s + 3}$

Answer & Explanation

unessodopunsep

Skilled2021-09-07Added 105 answers

Find the laplace transform of $L {t + e^{3 t}}$
definition of Laplace Transform of f(t)
$L {f (t)} = \int_{0}^{\infty} e^{- s t} f (t) d t$
Step 2
So
$L {t + e^{3 t}} = \int_{0}^{\infty} e^{- s t} (t + e^{3 t}) d t$
$= \int_{0}^{\infty} t e^{- s t} d t + \int_{0}^{\infty} e^{- (s - 3) t} d t$
$= {[t \frac{e^{- s t}}{- s} - \frac{e^{- s t}}{s^{2}}]}_{0}^{\infty} + {[\frac{e^{- (s - 3) t}}{- (s - 3)}]}_{0}^{\infty}$
$= (0 + 0 + 0 + \frac{1}{s^{2}}) + (0 + \frac{1}{s - 3})$
$∵ e^{- \infty} = 0$
$= \frac{1}{s^{2}} + \frac{1}{s - 3}$
$L {t + e^{3 t}} = \frac{1}{s^{2}} + \frac{1}{s - 3}$

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