Laplace Transform

Question 1

L{1}

Answer 1

1/s

Question 2

L{e^(bt)}

Answer 2

1/(s - b)

Question 3

L{sin(bt)}

Answer 3

b/(s^2 + b^2)

Question 4

L{cos(bt)}

Answer 4

s/(s^2 + b^2)

Question 5

L{f(bt)}

Answer 5

(1/|b|) * F(s/b)

Question 6

L{e^(bt) * f(t)}

Answer 6

F(s - b)

Question 7

L{f’(t)}

Answer 7

sF(s) - f(0)

Question 8

L{t * f(t)}

Answer 8

-F’(s)

Question 9

L{∫(from 0 to t) f(t) dt}

Answer 9

(1/s) * F(s)

Question 10

L{O(t)}

Answer 10

1/s

Question 11

L{δ(t)}

Answer 11

1

Question 12

L{t^k}

Answer 12

k! / s^(k+1)

Question 13

cos2v =

Answer 13

cos^2(v) - sin^2(v) // 2cos^2(v) - 1 // 1 - 2sin^2(v)

Question 14

sin2v =

Answer 14

2sin(v)cos(v)

Question 15

Cirkelns ekvation

Answer 15

(x-a)^2 + (y-b)^2 = r^2 // Där (a,b) är medelpunkten av cirkeln

Question 16

u’(x) + f(x)u(x) = g(x)

Answer 16

u(x) = e^(-F(x)) * (primitiv av) e ^(F(x) * g(x) dx

Question 17

g(u(x))u’(x) = f(x)

Answer 17

G(u(x)) = F(x) + C

Question 18

Rotationskropp runt X-axeln

Answer 18

V = pi (b till a) f(x)^2

Question 19

Rotationskropp runt Y-axeln

Answer 19

V = 2pi (b till a) x*f(x)

Question 20

ax^2u’’ + bxu’ + cu = 0

Answer 20

Två reella u(x) Ax^(r1) + Bx^(r2) // r1=r2 u(x) = Ax^r + Bln(x)x^r

Question 21

au’’ + bu’ + cu = 0

Answer 21

Två rella u(x) Ae^(r1x) + Be^(r2x) // r1 = r2 u(x) Ae^(rx) + Bxe^(rx)

Question 22

Integrera 1/(a-x)

Answer 22

-ln(∣a-x∣)

Question 23

Båglängd graf

Answer 23

L = (b till a) sqrt(1+ f’(x)^2 dx