Right Riemann Sum

Right Riemann Sum

Use the right endpoint of each subinterval:

$\sum_{i=1}^{n} f(a + i \cdot h) \cdot h \quad \text{where } h = \frac{b-a}{n}$

a    a+h  a+2h       b
|----|----|----|...|
     ^    ^         ^
     right endpoints used

Left vs. Right vs. Exact

For $\int_0^1 x^2\, dx = \frac{1}{3}$:

The left sum underestimates (for increasing $f$) and the right sum overestimates. The true integral is sandwiched between them:

$\text{riemann\_left}(f, a, b, n) \leq \int_a^b f(x)\, dx \leq \text{riemann\_right}(f, a, b, n)$

(assuming $f$ is increasing; swap inequality if decreasing)

Average of Left and Right

The average of the left and right Riemann sums is the trapezoidal rule (next lesson), which has $O(h^2)$ error.

Your Task

Implement double riemann_right(double (*f)(double), double a, double b, int n). The loop runs from $i=1$ to $i=n$ (inclusive).