Identify the various parts of the expression
Translate into symbols: "the integral of the function 2t + 3t2 on the interval [0, 2]."
We know the answer will look something like this:
We need to fill in all the pieces. We're taking the integral of the function 2t + 3t2, so that's our integrand:
Since this function uses the variable t, that's our variable of integration:
Since we're looking at the interval [0, 2], the lower limit of integration is 0 and the upper limit of integration is 2:
Let f (x) = 4x. Find .
It helps to look at a graph:
The area between f and the x-axis on this interval is a triangle with base 2 and height 8. We know the area of this triangle is
Let f (x) = 4x + 2. Find .
From the graph, we can see that this area splits nicely into a rectangle and a triangle:
Make it rain.
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