Question

Evaluate the integral.

integral of t sinh mt dt

Answer 1

the integral of sinh(mt) is cosh(mt)/m; so let's guess the answer is t cosh(mt)/m. take a derivative: we get cosh(mt)/m+t sinh(mt). cosh(mt)/m is just the derivative of sinh(mt)/m^2. thus t cosh(mt)/m-sinh(mt)/m^2 is the answer.

Answer 2

isn't the integral of sinx =-cosx

Answer 3

it is; sinh(x), however, is a hyperbolic function.

Answer 4

defined as (e^x+e^-x)/2. so the derivative of sinh(x) is cosh(x).

Answer 5

as is the integral.

Answer 6

o ok i didn't realize that thank you i understand the rest of the problem was just lost on why the negative disappeared

Answer 7

cool ;)