00:01
We are given an integral from 1 to 5 of function 5x - where the limits of integration are 1 and 5.
00:11
Now, break it into two parts and use geometric interpretation.
00:15
So the integral from 1 to 5, 5x dx, this part represents the area under the curve, area under the curve, y is equal to 5x, between 1 and 5.
00:34
So it is the area of a trapezoid with base is equal to 4 units from 1 to 5 and the height is equal to 20 units corresponding to the maximum value of the function at 5.
00:51
And the shorter base of 5 units corresponding to the value of the function at x is equal to 1.
00:57
Now, the formula to, formula to find the area, now the formula to find the area of the trapezoid is 1 over 2, sum of the bases multiplies the height.
01:15
The other base is 5 units.
01:19
So putting the values, we get area is equal to 1 over 2, the bases are 4 plus 5 multiplies the height is 20.
01:29
Now solving this, we get 9 multiplies 10 which is 90 units squared...