Suppose that the velocity function of a particle moving along a coordinate line is `v(t)=9t^3+4` Find the average velocity of the particle over the time interval `1lt=tlt=4` by integrating.

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The average value of a function over an interval [a,b] is `1/(b-a)int_a^b f(x)dx`

Here the interval is [1,4] and the function `v(t)=9t^3+4`

The average value is :

`1/3int_1^4(9t^3+4)dt`

`=1/3[9/4t^4+4t|_1^4 ]`

`=1/3[(576+16)-(9/4+4)]`

`=1/3[2343/4]`

`=781/4=195.25`

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