the voltage v (in volts) induced in a tape head is given by v=t^2e^3t, where t is the time (in seconds). find the average value of v over the interval from t=0 to t=2. Round to the nearest volt.

i need the work!!

Thank you for the opportunity to help you with your question!

Given the voltage v=t^2 e^3t

to find the average value of v in the interval from t=0 to t=2 is

average value of v = integral v dt

= integral ( t=0 to t=2) t^2 e^3t dt

= ( t=0 to t=2) (1 / 3)t^2*e^(3t) - (2 / 9)t*e^(3t) + (2 / 27)e^(3t)

now substitute value of t

we get = [(1/3)(2)^2 * e^6 - (2/9)2 * e^(3 *2) + (2/27)e^(3*2) ] -[ (1/3)(0)^2 *e^(3*0) -(2/9)0*e^(3*0) +(2/27)e^(3*0)

= (1/3)4*e^6 - (2/9)2e^6 + (2/27) e^6 - [0 -0+(2/27)*1 ]

= 4/3 * e^6 -4/9 e^6 +2/27e^6 -2/27

= [ 4*9 e^6 - 4*3 e^6 +2 e^6 -2 ] / 27

= [ 36 e^6 - 12e^6 + 2 e^6 - 2 ] / 27

= [ 46 e^6 - 2]/27

so average value is [ 46 e^6 - 2]/27

Hi user , I'm new to this study pool. If you have any doubts , Just comment

it tells me incorrect!!

one sec i will convert the answer into numerical value, Then it will work

ok thanks... i need the steps, thanks again!

yes...

so ok first i will expalain how to get the answer

average value of v = [46 e^6 -2 ]/27

=[ 46*404.961 - 2 ] / 27

=689.86 volts

rounding average value will be 690 volt

it saids incorrect!

ok thanks

so once you are done with the integartion

then we have to plug t=2 and t =0

so

=(1/3) t^2 * e^3t - (2/9) t * e^3t + (2/27)e^3t this what we got, now plug t values

= [ (1/3) (2)^2 * e^(3*2) - (2/9) 2* e^(3*2) + (2/27) e^(3*2) ] - [ 0 -0 + 2/27 ]

= [ 4/3 e^6 - 4/9 e^6 + 2/27 e^6 - 2/27]

= [4*9 e^6 - 4*3 e^6 +2 e^6 -2 ]/27

=[36 e^6 - 12 e^6 + 2 e^6 - 2 ] /27

= [ 26 e^6 - 2 ] / 27

so average value will be = [ 26 e^6 - 2 ] / 27*2

= [ 26 e^6 - 2]/ 54

it would be approximately 195 volt

194 will be fine?

if you have any doubt plug e =2.72 and calculate like 194.something

yes!! thank you very much!!

thanks a lot . If you have any questions in maths just ping me .

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up