3. Consider the function f(x): = x/3 5 a. (2 points) Use Wolfram Alpha to obtain...

  

Transcribed Image Text:

3. Consider the function f(x): = x/3 5 a. (2 points) Use Wolfram Alpha to obtain the numerical value of the definite integral I() = f f(x)dx. Submit a screenshot of the page showing the input and the result with at least 12 decimal places. b. (2 points) Complete the following MATLAB code to find the least positive integer N such that MN (f) I(f) < 10-6. (Recall that My is the composite midpoint rule.) % Question 3b I = % Enter the value from part (a) with at least 12 decimal places. f = @(x) % Complete the definition of the function f M = @(f, a, b, N) (b-a)/N*sum ( arrayfun (f, (a+ (b-a)/(2*N) *linspace (1, 2*N-1, N))) ); N = 0; Your code for searching for the desired N here. disp (N): solve Integrate[(x^1/3)/5, {x,0,7}] V NATURAL LANGUAGE Sa MATH INPUT Definite integral 0.35 0.30 0.25 0,20 0.15 0.10 0.05 0.00 x 21 7 dx = 5 20 Visual representation of the integral left sum 2 Riemann sums FROM THE MAKERS OF WOLFRAM LANGUAGE AND MATHEMATICA 3 4 2.00857774191101 5 6 7 Step-by-Step Solutions with Pro Get a step ahead with your homework Go Pro Now WolframAlpha (assuming subintervals of equal length) EXTENDED KEYBOARD EXAMPLES Fewer digits 7 7 (1) 4/ H-3 = 2137 77 +27 () 4/ (-) + 73/77 + 0(()^) 20 10n 5 180 n More digits UPLOAD RANDOM Step-by-step solution More cases H is the generalized harmonic number L(S) is the Riemann zeta function UPGRADE TO PRO DISCOVER WHAT'S POSSIBLE with Wolfram Alpha Take the Tour APPS TOUR Sign in 3. Consider the function f(x): = x/3 5 a. (2 points) Use Wolfram Alpha to obtain the numerical value of the definite integral I() = f f(x)dx. Submit a screenshot of the page showing the input and the result with at least 12 decimal places. b. (2 points) Complete the following MATLAB code to find the least positive integer N such that MN (f) I(f) < 10-6. (Recall that My is the composite midpoint rule.) % Question 3b I = % Enter the value from part (a) with at least 12 decimal places. f = @(x) % Complete the definition of the function f M = @(f, a, b, N) (b-a)/N*sum ( arrayfun (f, (a+ (b-a)/(2*N) *linspace (1, 2*N-1, N))) ); N = 0; Your code for searching for the desired N here. disp (N): solve Integrate[(x^1/3)/5, {x,0,7}] V NATURAL LANGUAGE Sa MATH INPUT Definite integral 0.35 0.30 0.25 0,20 0.15 0.10 0.05 0.00 x 21 7 dx = 5 20 Visual representation of the integral left sum 2 Riemann sums FROM THE MAKERS OF WOLFRAM LANGUAGE AND MATHEMATICA 3 4 2.00857774191101 5 6 7 Step-by-Step Solutions with Pro Get a step ahead with your homework Go Pro Now WolframAlpha (assuming subintervals of equal length) EXTENDED KEYBOARD EXAMPLES Fewer digits 7 7 (1) 4/ H-3 = 2137 77 +27 () 4/ (-) + 73/77 + 0(()^) 20 10n 5 180 n More digits UPLOAD RANDOM Step-by-step solution More cases H is the generalized harmonic number L(S) is the Riemann zeta function UPGRADE TO PRO DISCOVER WHAT'S POSSIBLE with Wolfram Alpha Take the Tour APPS TOUR Sign in