Here is a reasonable video of what you want.
https://www.youtube.com/watch?v=ghUVDEdtdpM
I don't like the way he abuses the equal sign and slaps his arithmetic all over the place
but the problems illustrates what happens when some of the area comes out as negative.
What is the difference between "area" and "net area" in calculus? I'm doing homework dealing with definite integrals and some problems ask for area and some ask for net area.
Thank you for your help in advance. 😀
4 answers
Thank you, I watched it and it helped me quite a bit. However, I'm now concerned that a problem like this will be on my final exam next week where I am not allowed to use a graphing calculator.
If that happens, just sketch the curve and break the integral into separate parts, subtracting the negative areas if necessary.
Back in the olden days, we did not have calculators of any kind.
As oobleck stated, it is a good idea to always make a sketch to have
a mental image of what the problem is.
Look if part of the graph is above and part is below the x-axis within your
integral boundaries. Often you will have to find the x-intercepts to see where
you must split your integrals. In the video I gave you, it was obvious that x = 1 was
the split.
As oobleck stated, it is a good idea to always make a sketch to have
a mental image of what the problem is.
Look if part of the graph is above and part is below the x-axis within your
integral boundaries. Often you will have to find the x-intercepts to see where
you must split your integrals. In the video I gave you, it was obvious that x = 1 was
the split.
11 answers