8. Definite Integrals

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.

Approximate the area under the curve $f\(\left\)(x\(\right\))=\(\frac{2}{3x+5}\)$ over the interval $\(\left\[\lbrack\)4,10\(\right\]\rbrack\)$ using the Midpoint Riemann sum with $n=3$ subintervals.

Evaluate the following summation: 

$\(\sum\)_{i=1}^4i^2-3i+8$

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

Evaluate the following summation: 

$\(\sum\)_{i=0}^2\(\frac{2i}{3}\)$

Evaluate the following summation: 

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

Evaluate the following summation: 

$\(\sum\)_{i=1}^24i^3-3i^2+2i-1$

Evaluate the following summation: 

$\(\sum\)_{t=2}^65t+\(\frac{4}{t}\)$

Evaluate the following summation: 

$\(\sum\)_{i=0}^42i+1$

Approximate the area under the curve $f\(\left\)(x\(\right\))=\(\sqrt{x+3}\)$ over the interval $\(\left\[\lbrack\)1,5\(\right\]\rbrack\)$ using the Right Riemann sum with 8 subintervals.