8. Definite Integrals

Evaluate the following summation: 

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

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 (make sure your calculator is in radian mode): 

${\sum }_{i=1}^4\sin \left(\frac{\pi i}{8}\right)$

{Use of Tech} Approximating definite integrals Complete the following steps for the given integral and the given value of n. 

(c) Calculate the left and right Riemann sums for the given value of n.

∫₃⁶ (1―2𝓍) d𝓍 ; n = 6

{Use of Tech} Approximating definite integrals Complete the following steps for the given integral and the given value of n. 

(d) Determine which Riemann sum (left or right) underestimates the value of the definite integral and which overestimates the value of the definite integral.

∫₃⁶ (1―2𝓍) d𝓍 ; n = 6

{Use of Tech} Approximating definite integrals Complete the following steps for the given integral and the given value of n. 

(c) Calculate the left and right Riemann sums for the given value of n.

∫₀² (𝓍²―2) d𝓍 ; n = 4

{Use of Tech} Approximating definite integrals Complete the following steps for the given integral and the given value of n. 

(d) Determine which Riemann sum (left or right) underestimates the value of the definite integral and which overestimates the value of the definite integral..

∫₀² (𝓍²―2) d𝓍 ; n = 4