00:01
Hi there, so for this problem we're given, we're told that a ball is launched straight up in the air for a height.
00:11
So we're given the initial height of this that is equal to six.
00:16
And its velocity is given by the function f of d.
00:22
That is equal to minus 32 times the time.
00:29
And this plus 280.
00:35
So the question is between the 10 seconds and the 12 .2 seconds, the ball's height change by what amount of feet? so first of all, consider that the speed is the rate of change of, in this case, the height with respect to time.
00:56
So if we want the expression for the height, we just take the integral of the function for the velocity integrated over the time.
01:08
So in this case, that will be the integral from 10 to 12 .2.
01:21
This of minus 32 times the time.
01:28
This plus 280.
01:30
This integrated over the time.
01:37
So we just need to solve this integral...