1
99:59:59,999 --> 99:59:59,999
so we've got the function f of x is equal

2
99:59:59,999 --> 99:59:59,999
to x squared, and what I am concerned with is finding

3
99:59:59,999 --> 99:59:59,999
the area under the curve y is equal to f of x

4
99:59:59,999 --> 99:59:59,999
that's my y-axis, this is my

5
99:59:59,999 --> 99:59:59,999
my x-axis, they'll let me draw my function

6
99:59:59,999 --> 99:59:59,999
my function looks like this, at least in the

7
99:59:59,999 --> 99:59:59,999
first quadrant, that's why I'll graph it for now, I could also graph it on the

8
99:59:59,999 --> 99:59:59,999
in the second quadrant, but what I care about is the area

9
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under this curve and above the positive x-axis

10
99:59:59,999 --> 99:59:59,999
between x equals 1 and x

11
99:59:59,999 --> 99:59:59,999
equals 4, and I'm tired of

12
99:59:59,999 --> 99:59:59,999
approximating areas, I want to find the exact area under this curve

13
99:59:59,999 --> 99:59:59,999
above the x-axis, and the way we didn't know

14
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the exact area under the curve, this little brown shaded area

15
99:59:59,999 --> 99:59:59,999
is using the definite integral, the definite integral from 1 to 4