8. Definite Integrals

Evaluate the following summation: 

$\sum_{i=1}^4i^2-3i+8$

Evaluate the following summation: 

$\sum_{k=1}^4\left(\frac{k}{_{}2}\right)^2$

Evaluate the following summation: 

$\sum_{i=0}^2\frac{2i}{3}$

Evaluate the following summation: 

$\sum_{t=2}^65t+\frac{4}{t}$

Evaluate the following summation: 

$\sum_{i=0}^42i+1$

Evaluate the following summation: 

$\sum_{i=1}^24i^3-3i^2+2i-1$

For the following graph, write a Reimann sum using left endpoints to approximate the area under the curve over [0,5] with 5 subintervals.

For the following graph, write a Reimann sum using left endpoints to approximate the area under the curve over [0,6] with 6 subintervals.

Write the Riemann sum that would approximate the area of the following graph over the interval [0,3] using 3 subintervals.

Approximate the area under the curve $f\left(x\right)=\sqrt{x+3}$ over the interval $\left\lbrack1,5\right\rbrack$ using the Right Riemann sum with 8 subintervals.

Approximate the area under the curve $f\left(x\right)=\frac{2}{3x+5}$ over the interval $\left\lbrack4,10\right\rbrack$ using the Midpoint Riemann sum with $n=3$ subintervals.