Answer:
a)550
b)910
c)730
Explanation:
The given model is

Use the interval [0,6], with n=6 rectangles
Then, the interval width is

= 1
so, the sub intervals are
[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]
Now evaluating the function values







a) left hand sum is
L_6 =
![\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)]](https://img.qammunity.org/2020/formulas/mathematics/high-school/jc7iy37x6occ7blue7zgu315u9mkazacvw.png)
=
![1 [0+ 10+40+90+160+250]](https://img.qammunity.org/2020/formulas/mathematics/high-school/5kx92kmxec5nu4mdxrwlsfw8f8wnsokora.png)
= 550
b) right hand sum
R_6 =
![\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)]](https://img.qammunity.org/2020/formulas/mathematics/high-school/b4965ciwzaj0993k0rry5jf5f4d7d70plt.png)
=
![1 [10+40+90+160+250+360]](https://img.qammunity.org/2020/formulas/mathematics/high-school/zqjaw4bwco7ckbi3xlcbhh949mwi55vtmj.png)
= 910
c) average of two sums is

=

=730