Calculus BC Question, Need Help ASAP

Question

Write the Riemann sum to find the area under the graph of the function f(x) = x⁴ from x = 5 to x = 7.

Answer 1

Joy

To find a Riemann sum we split the x interval into intervals of same width.

Let's say we use 4 intervals here.

so intervals will be [5, 5.5], [5.5, 6], [6. 6.5] [6.5, 7]

To find the right Riemann sum, find the function at the right end of the interval and multiply by interval width then add them all up.

So right Riemann sum here is 0.5 f(5.5) + 0.5 f (6) + 0.5 f (6.5) + 0.5 f (7)

You can figure this out yourself

The left Riemann sum, same idea but you evaluate f(x) at the left end of the intervals, at 5, 5.5, 6, 6.5

Mike