Let $y = \frac { 1 } { 4 }x^4 − 3x^2 − 1$.

1. Use seven left endpoint rectangles to approximate the area under curve over the interval $0 ≤ x ≤ 2.5$.

   Step 1(a):

   rectangle width: $\frac{2.5-0}{7}=\:?$

   Step 2(a):

   endpoints: $x_0 = 0, x_1 = \frac{5}{14}, x_2 = \frac{10}{14}, ..., x_n = \:?$

   Step 3(a):

   $\displaystyle \sum _ { n = 0 } ^ { 6 } \frac { 2.5 } { 7 }f(x_n)$

2. Approximate the area under the curve over the interval $–2.5 ≤ x ≤ 2.5$. Explain how you determined your answer.