approximate the area under f(x) = 10x - x2, above the x-axis, on [1,7] with n...

approximate the area under f(x) = 10x - x², above the x-axis, on [1,7] with n = 6 rectangles using the left and right endpoint, trapezoidal rule and midpoint methods (include summation notation and endpoint values) and then find the exact area using a definite integral (include a graph with shaded region)

Expert Solution

milcah answered 2 years ago

Approximate the area under f(x) = (x – 1)2, above the x-axis, on [2,4] with n...

Approximate the area under f(x) = (x – 1)2, above the x-axis, on [2,4] with n = 4 rectangles using the (a) left endpoint, (b) right endpoint and (c) trapezoidal rule (i.e. the “average” shortcut). Be sure to include endpoint values and write summation notation for (a) and (b). Also, on (c), state whether the answer over- or underestimates the exact area and why.

Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the...

Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the following methods with n=4. f(x)=88x+55 from x=44 to x=66 a. Use left endpoints. b. Use right endpoints. c. Average the answers in parts a and b. d. Use midpoints.

Consider the following. f(x) = x(x2 - 10x + 30) g(x) = x2

Consider the following. f(x) = x(x2 - 10x + 30) g(x) = x2 (a) Use a graphing utility to graph the region bounded by the graphs of the functions.(b) ) Find the area of the region analytically (c) Use the integration capabilities of the graphing utility to verify your results.

Use finite approximation to estimate the area under the graph f(x)= 8x2 and above graph f(x)...

Use finite approximation to estimate the area under the graph f(x)= 8x2 and above graph f(x) = 0 from X0 = 0 to Xn = 16 using i) lower sum with two rectangles of equal width ii) lower sum with four rectangles of equal width iii) upper sum with two rectangles of equal width iv) upper sum with four rectangle of equal width

Find the approximate area under the curve by dividing the intervals into n subintervals and then...

Find the approximate area under the curve by dividing the intervals into n subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x. Your instructor will assign you n_1 = 4 and n_2 = 8. 1. y=2x√(x^2+1) Between x = 0 and x = 6 for n1 = 4, and n2 = 8 2. Find the exact area under the curve using...

Find the approximate area under the curve by dividing the intervals into (n) subintervals and then...

Find the approximate area under the curve by dividing the intervals into (n) subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x. Your instructor will assign you (n1) and (n2) y = 2x square root x^2 + 1 between x = 0 and x = 6 for n1 = 4 and n2 = 8 Find the exact area under the curve...

f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the...

f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the region completely enclosed by the graphs of the given functions f and g in square units.

Approximate the area under the graph of f(x)=0.03x4−1.44x2+58 over the interval [2,10] by dividing the interval...

Approximate the area under the graph of f(x)=0.03x4−1.44x2+58 over the interval [2,10] by dividing the interval into 4 subintervals. Use the left endpoint of each subinterval. The area under the graph of f(x)=0.03x4−1.44x2+58 over the interval [2,10] is approximately ...

Describe a probability distribution. Explain the x-axis, y-axis, and area under the distribution.

state the area between the lorenz curve L(x)=xe^(x-1) and the x-axis as a definite integral. Approximate...

state the area between the lorenz curve L(x)=xe^(x-1) and the x-axis as a definite integral. Approximate its value (to 3 decimal places) using midpoints and n=5 equal with subintervals.

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