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**R3ap3r** Find the approximate area between the curve $\displaystyle y = 12x - 2x^2$ and the x-axis, from $\displaystyle x = 0$ to $\displaystyle x=5$ using 5 inscribed rectangles of equal width.

**My Work:**

$\displaystyle n = 5$

$\displaystyle y = 12x - 2x^2$

$\displaystyle x = 0\; y_0 = 0$

$\displaystyle x = 1\; y_1 = 10$

$\displaystyle x = 2\; y_2 = 16$

$\displaystyle x = 3\; y_3 = 18$

$\displaystyle x = 4\; y_4 = 16$

$\displaystyle x = 5\; y_5 = 10$

$\displaystyle .5h[(y_0 + y_n) + 2(y_1 + y_2 +\; ...\; y_{n - 1})]$

$\displaystyle .5\cdot .5[(0 + 10) + 2(10 + 16 + 18 + 16)] = 32.5$

$\displaystyle area\; is\; 32.5\; units^2$

Hows it look?