1. Consider the function f (x) = x5 - 4x+4x + 4 over the interval [-1,0]....

 

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1. Consider the function f (x) = x5 - 4x+4x + 4 over the interval [-1,0]. a) Determine the right-hand Riemann sum. Will this be an overestimate or an underestimate? b) Determine the left-hand Riemann sum. Will this be an overestimate or an underestimate? c) Determine the midpoint Riemann sum. Will this be an overestimate or an underestimate? d) Calculate f(x5 - 4x + 4x +4) dx e) Calculate the error between the integral and the Riemann sums calculated in steps a-c. 2. Rewrite the given infinite sum as an integral, then use Desmos or your graphing calculator to evaluate the integral. Justify your answer. lim ( (-)* + 4 () - ) () n0 i=1 3. Rewrite the given integral as an infinite sum, then use Desmos or your graphing calculator to evaluate the integral. Justify your answer. TC [ sin (x) dx 1. Consider the function f (x) = x5 - 4x+4x + 4 over the interval [-1,0]. a) Determine the right-hand Riemann sum. Will this be an overestimate or an underestimate? b) Determine the left-hand Riemann sum. Will this be an overestimate or an underestimate? c) Determine the midpoint Riemann sum. Will this be an overestimate or an underestimate? d) Calculate f(x5 - 4x + 4x +4) dx e) Calculate the error between the integral and the Riemann sums calculated in steps a-c. 2. Rewrite the given infinite sum as an integral, then use Desmos or your graphing calculator to evaluate the integral. Justify your answer. lim ( (-)* + 4 () - ) () n0 i=1 3. Rewrite the given integral as an infinite sum, then use Desmos or your graphing calculator to evaluate the integral. Justify your answer. TC [ sin (x) dx