duuuuuuuuuuuuuuuuuuuuuuuuude, the super bowl was boring
anyway, we didn't learn a single new thing this week, so what am I supposed to blog about?
something: !
Ex. Find the area of the region bounded by the curve f(x) = x² and the x-axis between x=0 and x=3. Use 3 rectangles.
First of all, x=0 and x=3 are your bounds. So to rewrite this equation, it would be: 3S0 x² dx. (*”S” is the integral symbol.)
Next, what is the width? To find it, subtract your upper and lower bounds, then divide by the number of rectangles: (3-0)/3 = 1
Now, to find the lengths, plug in to the original equation every number between 0 and 3 that is 1 width away. The numbers will be 0, 1, 2, and 3. To plug in: (0)² = 0; (1)² = 1; (2)² = 4; (3)² = 9
Finally, for LRAM, multiply the width by the first three lengths (all of the left points) and add them together: (1)(0) + (1)(1) + (1)(4) = 5
For RRAM, multiply the width by the last three lengths (all of the right points) and add them together: (1)(1) + (1)(4) + (1)(9) = 14
Your answer: 5 < area < 14
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