Integration by parts of a function

[apiwowar]

the function is c = 15te^-.2t

the goal is to integrate it from t = 0 to t = 3

so to set up the integral i took out the 15 first so i got:

15 * integral from 0 to 3 of t*e^-.2t

i set u = t and so du = dt
dv = e^-.2tdt so v= -5e^-.2t

so following the integration by parts formula i got:

15(-5*e^-.2t + 5* integral of e^-.2tdt

then after integrating the second part i got

15(-5e^-.2t - 25e^-.2t) evaluated from 0 to 3

when evaluated i got

(-123/4826181 - 205.8043635)-(-75-375) = 120.7130184

but that's wrong,

anyone have any hints or sees any mistakes that i made?

thanks

 

[rock.freak667]

the function is c = 15te^-.2t

the goal is to integrate it from t = 0 to t = 3

so to set up the integral i took out the 15 first so i got:

15 * integral from 0 to 3 of t*e^-.2t

i set u = t and so du = dt
dv = e^-.2tdt so v= -5e^-.2t

so following the integration by parts formula i got:

15(-5*e^-.2t + 5* integral of e^-.2tdt
s

this should be

15(-5te^-0.2t+5∫e^-.2tdt

 

[apiwowar]

your right, that's just a typo, i had the t there in my calculations

 

[rock.freak667]

it looks like you did it correct, is your answer supposed to be in terms of e?

 

[apiwowar]

i don't think so, it just asks for the exact answer

 

[rock.freak667]

i don't think so, it just asks for the exact answer

Then you need to write it in terms of the constant e. So recalculate the answer, just not using a calculator.

 

[apiwowar]

so just leave it as with the base e but calculate the exponents of e?

 

[rock.freak667]

so just leave it as with the base e but calculate the exponents of e?

Yes.

 

[apiwowar]

ok, thanks a lot