CPM Homework Help : CALC3RD Problem 9-50

Using summation notation, write a Riemann sum to represent the area under $f(x) = 2\cos^2(x) - x$ from $-\frac { \pi } { 2 }≤ x ≤\frac { \pi } { 2 }$ using six left endpoint rectangles.

Hint:

The length of the interval is $π$ . Using $6$ rectangles, what is the width of each rectangle?

Step:

$\displaystyle \sum_{i=0}^5\frac{\pi}{6}f\Big(-\frac{\pi}{2}+\frac{\pi i}{6}\Big)$