Thread: Evaluating integrals in terms of area without a visual aid/graph

How would you go about doing this? I'm specifically trying to evaluate the integral from -3 to 2 of (3-4x)dx. I know this will involve triangles but how am I supposed to know the specs of the triangles without a graph?

Why you should do it without a graph?

Anyways, you just need to evaluate the function in the limits to the triangles heights, and know when so you can get the base of the triangles.

I'm just wondering if there is a way to do it without a graph, because it seems like on my worksheet it's implying that a graph isn't needed because our professor said she left enough space between each problem to do the work associated with the problem, to clue us in if we were going about it in a way that's too long or too UNdetailed, and for this problem there's only 3 line spaces, certainly no room for a graph so I'm assuming there's a way to do it without a graph?

Personally, I'm able to picture the general shape of graphs in my mind. I don't know if others do this but I can.

In your example, Y = -4x + 3. Recall the standard line graph of Y = mx + b. M is the slope and b is the y-intercept. Since the slope is negative, that means you can picture the graph coming in a southeastern direction from the y-axis to the x-axis.