Saturday

August 2, 2014

August 2, 2014

Posted by **Nycw** on Friday, February 1, 2013 at 10:15pm.

- calculus 2 -
**Eman**, Friday, February 1, 2013 at 10:32pmRevolved about the x-axis~ must use: integral 2*Pi*y ds (Eq 1)

For ds use:

ds = sqrt(1+[F'(x)]^2) dx (Eq 2)

sinh(x) dx = cosh(x) = F'(x)

sub cosh(x) into Eq 2 and you get:

ds = sqrt(1+[cosh(x)]^2) dx

now sub ds into Eq 1

integral 2*Pi*y*sqrt(1+[cosh(x)]^2) dx

We are taking the derivative with respect to x so change y to it's equivalent.

integral 2*Pi*sinh(x)*sqrt(1+[cosh(x)]^2) dx, from 0 to 1

you now have your final equation to integrate over the interval, 0 to 1

and you get 5.52989 (final answer)

- calculus 2 -
**Eman**, Friday, February 1, 2013 at 10:33pmRevolved about the x-axis~ must use: integral 2*Pi*y ds (Eq 1)

For ds use:

ds = sqrt(1+[F'(x)]^2) dx (Eq 2)

sinh(x) dx = cosh(x) = F'(x)

sub cosh(x) into Eq 2 and you get:

ds = sqrt(1+[cosh(x)]^2) dx

now sub ds into Eq 1

integral 2*Pi*y*sqrt(1+[cosh(x)]^2) dx

We are taking the derivative with respect to x so change y to it's equivalent.

integral 2*Pi*sinh(x)*sqrt(1+[cosh(x)]^2) dx, from 0 to 1

you now have your final equation to integrate over the interval, 0 to 1

and you get 5.52989 (final answer)

- calculus 2 -
**Reiny**, Friday, February 1, 2013 at 10:35pmby definition

sinh(x) = (e^x - e^-x)/2

so the area

= ∫sinh(x) dx from 0 to 1

= ∫(e^x - e^-x)/2 dx from 0 to 1

= [ e^x + e^-x)/2] from 0 to 1

= (e^1 + e^-1)/2 - (e^0 + e^0)/2

= (e + 1/e)/2 - (1+1)/2

= e/2 + 1/(2e) - 1

= (e^2 + 1 - 2e)/(2e)

= (e - 1)^2 / (2e)

you better check my arithmetic

- totally ignore my post - calculus 2 -
**Reiny**, Friday, February 1, 2013 at 10:37pmscrap my reply,

I found the area, silly me

**Related Questions**

Calculus - Suppose that the region between the x-axis and the curve y=e^-x for x...

Solids of Revolution - The region enclosed by the curve y =e^x, the x-axis, and ...

calculus - The given curve is rotated about the y-axis. Find the area of the ...

calculus 2 - The region bounded by y=e^(-x^2),y=0 ,x=0 ,x=1 and is revolved ...

Calculus - The graph of the curve y2=10 x+10 is a parabola, symmetric with ...

Calculus HELP plz - Find the area of the surface obtained by rotating the curve ...

calculus II SURFACE AREA Integration - Find the exact area of the surface ...

calculus - if the region enclosed by the y-axis, the line y=2 and the curve y=...

Calculus I - Find the exact area of the surface obtained by rotating the curve ...

Calculus I - Find the exact area of the surface obtained by rotating the curve ...