Construct and simplify a sum approximating the area above the x-axis and under the curve y...
(1 point) Definition: The AREA A of the region that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x)Ar + f(x2)Ax+... +f(x,y)Ax] 100 Wspacelin (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x3 from x = 0 to x = 2. 64 A. lim 7100 11 i= B....
Use finite approximation to estimate the area under the graph of f(x) = x² and above the graph of f(x) = 0 from Xo = 0 to x = 4 using i) a lower sum with two rectangles of equal width ii) a lower sum with four rectangles of equal width ii) an upper sum with two rectangles of equal width iv) an upper sum with four rectangles of equal width The estimated area using a lower sum with two...
Use finite approximation to estimate the area under the graph of f(x) = 9x? and above the graph of f(x) = O from xo + 0 to x = 4 using i) a lower sum with two rectangles of equal width ii) a lower sum with four rectangles of equal width ii) an upper sum with two rectangles of equal width. iv) an upper sum with four rectangles of equal width. The estimated area using a lower sum with two...
3. Find the sum of the areas of approximating rectangles for the area under f(x) = 48 - x?, between x = 1 and x = 5 using 4 subintervals and the right endpoints of each subinterval for sample points.
3. Find the sum of the areas of approximating rectangles for the area under f(x) = 48 - x?, between x = 1 and x = 5 using 4 subintervals and the right endpoints of each subinterval for sample points. 31
Approximate the area under the following curve and above the x-axis on the given interval, using rectangles whose height is the value of the function at the left side of the rectangle (a) Use two rectangles. (b) Use four rectangles. (c) Use a graphing calculator (or other technology) and 40 rectangles. f(x)-2-x-1,1 (a) The approximated area when using two rectangles is square units (Type an integer or decimal rounded to two decimal places as needed.) (b) The approximated area when...
Use finite approximation to estimate the area under the graph of f(x) =x2 and above the graph of f(x) = 0 from x0-0 to xn-14 using i) a lower sum with two rectangles of equal width. ii) a lower sum with four rectangles of equal width ili) an upper sum with two rectangles of equal width iv) an upper sum with four rectangles of equal width. The estimated area using a lower sum with two rectangles of equal width is...
QUESTION 1 To compute the area below the curve f(x), above the x-axis, from x a to x-b, choose all correct answers The definite integral, f(x)dx, can be used to compute the area if f(x) 20 on the interval (a,b). The definite integral, f(x)dx, can be used to compute the area if f(x) > 0 on the interval [a,b]. The region was broken up into n rectangles and the sum of the areas of the rectangles was computed as n...
f(x) = 3/x+4, from x = 1 to x = 9 Approximate the area under the graph of f(x) and above the X-axis with rectangles, using the following methods with n=4. (a) Use left endpoints. (b) Use right endpoints. (c) Average the answers in parts (a) and (b) (d) Use midpoints. The area, approximated using the left endpoints, is _______ (Round to two decimal places as needed.)
(a) Estimate the area under the graph of f(x) = 4 + 4x2 from x = -1 to x = 2 using three rectangles and right endpoints. R3 = 32 Then improve your estimate by using six rectangles. RG :- 27.5 Sketch the curve and the approximating rectangles for R3. у 20 у 20 15 15 10 10 O-1 2 у у 20 20 15 15 10 10 5 -1 1 2 1 2 Sketch the curve and the approximating...