Question

Approximate the area under the curve y = x^3 + 1 from x = 0 to x = 3 using a left sum with 6 subdivisions.

The area is approximately?

Answer 1

well, I am not going to go through the pain of approximation with rectangles but your result should be something like the integral which is x^4/4 + x at 3 minus at 0
(81 / 4) + 3 - 0 = 23.25

Answer 2

so, each rectangle has width 1/2. That makes the area
1/2 (f(0) + f(1/2) + ... + f(5/2))
So plug and chug,

There are several handy Riemann sum calculators online for you to check your work.