- #1
d3nat
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two questions.
I know I'm doing the work right, but I can't get my answers to match and they are pretty close. I think it's just some arithmetic errors.
Help? I've been trying to solve my mistakes forever. I can't find them!
Use the parametric equation of an ellipse x = acos(t) and y=bsin(t) from 0<t<2PI (those are or equal to signs)
A=INTEGRAL from 0 - 2PI ydx
INTEGRAL from 0-2PI bsin(t)(-asin(t) dt
= -ab INTEGRAL 0 -2PI sin^2(t) dt
= -ab EVALUATED 1/2 (t) - 1/4*sin(2t) from 0-2PI
= -ab ((1/2*(2PI) - 1/4 (sin(2*2PI) - 0)
= -abPI
But the answer is abPI. I don't know where the negative sign goes... or if I am supposed to have another one that cancels mine out
Find the exact length of the curve
x = 1+3t^2
y= 4+2t^3
0<t<1 (or equal)
)^2)
L= INTEGRAL from a - b SQUARE ROOT (dx/dt)^2 +(dy/dt)^2 END SQUARE ROOT dt
dx/dt = 6t
dy/dt = 6t^2
L= INTEGRAL from 0-1 SQARE ROOT (6t)^2 + (6t^2)^2 END SQUARE ROOT dt
= 6 INTEGRAL from 0-1 t* SR 1+t^2 dt
using u substitution
u = 1+t^2
du = 2t dt
boundaries change to 1 - 2
= 3 * integral from 1-2 square root u du
= 3 * 2*u^3/2 evaluated from 1-2
= 3 * ( 2(2)^3/2 - 2(1)^3/2 )
= 3 * (4 square root (2) - 2)
= 12 square root (2) - 6
answer is supposed to be
4 square root (2) - 1
I know I'm doing the work right, but I can't get my answers to match and they are pretty close. I think it's just some arithmetic errors.
Help? I've been trying to solve my mistakes forever. I can't find them!
Homework Statement
Use the parametric equation of an ellipse x = acos(t) and y=bsin(t) from 0<t<2PI (those are or equal to signs)
Homework Equations
A=INTEGRAL from 0 - 2PI ydx
The Attempt at a Solution
INTEGRAL from 0-2PI bsin(t)(-asin(t) dt
= -ab INTEGRAL 0 -2PI sin^2(t) dt
= -ab EVALUATED 1/2 (t) - 1/4*sin(2t) from 0-2PI
= -ab ((1/2*(2PI) - 1/4 (sin(2*2PI) - 0)
= -abPI
But the answer is abPI. I don't know where the negative sign goes... or if I am supposed to have another one that cancels mine out
Homework Statement
Find the exact length of the curve
Homework Equations
x = 1+3t^2
y= 4+2t^3
0<t<1 (or equal)
)^2)
L= INTEGRAL from a - b SQUARE ROOT (dx/dt)^2 +(dy/dt)^2 END SQUARE ROOT dt
The Attempt at a Solution
dx/dt = 6t
dy/dt = 6t^2
L= INTEGRAL from 0-1 SQARE ROOT (6t)^2 + (6t^2)^2 END SQUARE ROOT dt
= 6 INTEGRAL from 0-1 t* SR 1+t^2 dt
using u substitution
u = 1+t^2
du = 2t dt
boundaries change to 1 - 2
= 3 * integral from 1-2 square root u du
= 3 * 2*u^3/2 evaluated from 1-2
= 3 * ( 2(2)^3/2 - 2(1)^3/2 )
= 3 * (4 square root (2) - 2)
= 12 square root (2) - 6
answer is supposed to be
4 square root (2) - 1