### Home > CALC > Chapter 5 > Lesson 5.1.2 > Problem5-19

5-19.

For $g(x)$ below, write and use your calculator to evaluate a Riemann sum to estimate $A(g,-4 ≤ x ≤ 4)$ for the functions below with $16$ rectangles. Recall that a Riemann sum does not have to involve sigma notation.

1. $g(x) = x\operatorname{ sin}^2 x$

General form of a right-endpoint Riemann sum:

1. $g ( x ) = \left\{ \begin{array} { c } { 3 \text { for } x < 0 } \\ { x ^ { 2 } + 3 \text { for } x \geq 0 } \end{array} \right.$

Your Riemann sum will need to split into two parts.

$A(g) = 42.25$