### Home > CALC3RD > Chapter Ch9 > Lesson 9.3.2 > Problem9-96

9-96.

Approximate the area under $f(x) = 2 \cos\sqrt { x }+3$ for $0 ≤ x ≤ 3$ using six midpoint rectangles of equal width.

The width of each rectangle will be $0.5$, so using midpoints:

$x_i=\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4},\frac{11}{4}$

$A\approx\frac{1}{2}\Big(2\cos\sqrt{\frac{1}{4}}+2\cos\sqrt{\frac{3}{4}}+2\cos\sqrt{\frac{5}{4}}+...\Big)$