<span>integral of (e^3x)/((e^6x)+1) dx = (e^6 x - log(e^6 x + 1))/e^9 + c</span>
Answer: Choice D) 0
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Explanation:
The interval [-2,2] is the same as writing -2 <= x <= 2 where "<=" without quotes means "less than or equal to"
Focus on the lower bound of the interval (x = -2). If x = -2, then y = 4 giving us the point (-2,4) on this parabola. You can draw a vertical line through x = -2 on the x axis and you'll see this vertical line crossing the parabola at (-2,4)
Similarly, the point (2,4) also lies on the parabola. This time we use the x value x = 2 as this is the upper part of the interval.
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So we'll use the two points (-2,4) and (2,4) to find the slope of the line through these points
m = (y2 - y1)/(x2 - x1)
m = (4 - 4)/(2 - (-2))
m = (4 - 4)/(2 + 2)
m = (0)/(4)
m = 0
The slope of this line is 0. Therefore the average rate of change on the interval [-2,2] is 0.
This is why the answer is choice D.
Side Note: the line that goes through the points (-2,4) and (2,4) is a completely flat horizontal line. All horizontal lines have slope 0.
Yes you can see the answer but you might need to watch an ad first then it will show you the answer
Since y=k, there is a slope of zero, which is just a horizontal line k units from the x-axis. In this case k=-5, so the graph of y=-5 is a horizontal line 5 units below the x-axis...