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These approximation rectangles such as LRAM, RRAM, MRAM are an extremely important part in understanding integrals. So as a heads up, this is an important foundational lesson.
For this problem, left rectangles, or LRAM, match the left corner of the rectangle to f(x). So you are adding rectangles in each step you do. So lets start with the first value. Since you need to line up the height of the rectangle to the leftmost side, that includes the first value. You have your height of the rectangle now, but you need to multiply by a width. On the graph/table, that width is the difference between the start and stop of your rectangle aka a step. Making 6 rectangles with 7 values makes it necessary to put a rectangle between each step in the data, so your first rectangle width becomes 3-1, or 2. You do this 6 times, finding the left hand height of the rectangle then finding the width.
f(x)= ∑(left hand height)(width)= 4*2 + 8*1 + 6*2 +....
Add it all up and you should get an answer of 70
