Question

Riemann Sums

Answer 1

integral of |x| from -2 to 2?

Answer 2

4?

Answer 3

\[\int\limits_{a}^{b}f(x)dx=\lim_{n \rightarrow \infty}\frac{ b-a }{ n }\sum_{i=1}^{n}f(a+\frac{ b-a }{ n }i)=\lim_{n \rightarrow \infty}\Delta \sum_{i=1}^{n}f(a+i \Delta)\]

\[-2+\frac{ 10i }{ n }=a+i \Delta ; a=-2 ; \Delta=\frac{ 10 }{ n }=\frac{ b-a }{ n }; b=8\]

\[f(a+i \Delta)=\frac{ \left| a+i \Delta \right| }{ 2 }-1 \]
\[f(x)=\frac{ \left| x \right| }{ 2 }-1=\int\limits_{-2}^{8}(\frac{ \left| x \right| }{ 2 }-1)dx\]

Answer 4

how do u solve the integral for the last part? is there any other way other than plotting graphs?

Answer 5

^ oh shoot wrong qn, my solution is for this qn