### Home > PC3 > Chapter 10 > Lesson 10.2.1 > Problem10-112

10-112.

Given $f(x) = x^2 + 3$, approximate $A( f , 3 ≤ x ≤ 6)$ using five left endpoint rectangles.

Sketch the curve, showing the rectangles used to approximate the area. Use sigma notation to write an expression for the specified area. Determine if the approximation is an underestimate or an overestimate for the actual area.

The width of the interval is $3$ and there are five rectangles, so the width of each rectangle is $0.6$.

The endpoints of the rectangles are $3, 3.6, 4.2, 4.8,$ and $5.4$. Write an expression for this sequence, $x_{n}$.

$A=\displaystyle \sum _ { n = 0 } ^ { 5 }0.6f(x_n)$