Question

Riemann Integral/The Definite Integral help? @Calculus1

Answer 1

I don't understand how to solve these by hand for example f(x)=sin (x) on the interval [0,pi] when n=8

Answer 2

are you using right hand endpoints or something else?

Answer 3

The exact question is Estimate the area under a single loop of the sine curve sin(x) by erecting on the region 8 circumscribed rectangles of equal width.

Answer 4

well there are may ways to do this. you can really pick and points in the partition of your interval...I'm going to go with right hand endpoints

so let \[x_i=i\cdot\Delta x\]

where \[i=1,2,\ldots 8\]

and \[\Delta x=\frac{\pi}{8}\]

then compute

\[\sum_{i=1}^{8}\sin(x_i)\Delta x\]

Answer 5

perfect, thank you