Consider the functions $f(x) = x^{2} + 2$ and $g(x) = x^3$. 

1. Is $f$ even, odd, or neither? Justify your answer algebraically.

2. Is $g$ even, odd, or neither? Justify your answer algebraically.

3. Approximate the area under $y = f(x)$ over the interval $−5 ≤ x ≤ 5$. Clearly show your method.

   Hint (c):

   Choose a number of rectangles, say $20$. Then each rectangle will have a width of $0.5$. The height will be $f(−5 + 0.5n)$. Calculate:

   $\displaystyle \sum _ {n=0}^{19}0.5f(-5+0.5n)\:\text{ OR }\:\displaystyle \sum _ {n=1}^{20}0.5f(-5+0.5n)$

4. Approximate the area under $y = g(x)$ over the interval $−5 ≤ x ≤ 5$. Clearly show your method.

   Hint: (d):

   Sketch the curve and then sketch some rectangles in the given interval. What do you notice?