Integrals are a breeze for me to solve, but graphing them is another thing. Why

Question

Integrals are a breeze for me to solve, but graphing them is another thing. Why is it that when I graph part a) on Wolfram Alpha, it only goes as far as the [-4, 4] ? So, I would need to sketch the graph of f(x) from [-6, 6], not the integral, is that correct?

Also, does part b) refer to the integral of f(x) and sketching that graph from 0 to x? If so, wouldn't I get an individual value, because it is a definite integral?

And to summarize: the graph for part a) is the function from -6 to 6, and the graph for part b) is the function after it is integrated from 0 to x, is that right?

Consider the function Sketch a graph of f(x) on the interval [-6, 6]. Find d/dx f(x) and sketch the graph. Using the graphs, find one local maximum and one local minimum.

Explanation / Answer

Hi,

1.f(x) IS the integral. So plotting curve of f(x) is the same as plotting curve of the integral. It is true that wolfram alphs is not providing full range you desire, but you can more or less extend the graph. Right?

2.here, you are supposed to find the differntiation of the integral, It is a bit different when the limits of integration are functions themselves. Please refer to http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign for the formula. You are supposed to plot the RESULTANT function whatever it is and plot that.

3. Graph of part 1 is the function, but graph of part 2 is as explained above.

To find maxima and minima of f(x), you want the derivative of f(x) which is obtained in part 2. Equate that to 0 to get points of extrema and proceed from ther.

Hope that helps.

Feel free to ask any doubts that are remaining.

thanks.

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