Find an approximation of the area of the region R under the graph of the function f on the interval [−1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 5 − x2

Q: Let f (x) = cos x − sin x for 0 ≤ x ≤ π/3.Find the area A of the region between the graph of f and…

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Q: Set up the definite integral required to find the area of the region between the graph of y=x2-17…

A: First draw the curves and find their intersection  points then use integration to get the area.

Q: Find the area between y = (3 + x2)e2x and the x­-axis from x = 0 to x = 1.

A: We have to find the area between y = (3 + x2)e2x and the x­-axis from x = 0 to x = 1   for that we…

Q: Let f (x) = 1/x  and g(x) = 1/x^2  Find the area A of the region between the graphs of f and g on…

A: f(x)=1x and g(x)=1x2To Find: the area A of the region between the graphs of f and g on the interval…

Q: Find the area between the graph of the function and the x-axis over the given interval, if possible.…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 18 -…

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Q: Find the area of the region under the graph of the function f on the interval [4, 11]. f(x) = 2x - 2…

A: use integral to evaluate the are bounded by curve over the interval

Q: Find the area of the region under the graph of f on [a, b]. f(x) = 3/x^2 ; [1, 4]

A: To find the area of the region under the graph of f on [a, b]. f(x) = 3/x^2

Q: 3. Approximate the area under the curve y =x² +2 between x = 1 and x=7 using 3 subintervals (n = 3)…

A: We know that according to right end approximation, the area under the curve is, A≈∑i=1nf(xi)∆x   It…

Q: Find the area of the region under the graph of f(x) = ln(x) from x = 3 to x = 11.

A: Given function : f(x) = ln(x) To find the area of the region from x=3 to x=11 To find the area of…

Q: Q1. Use r; as the right endpoint of each subinterval to find the area under the graph of f(x) = 9 -…

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Q: Find the area A of the region R between the graph of f(x)= (x^2)/(4-x^2)^(1/2) and the x-axis on the…

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Q: Find the area of the region under the graph of f(x) = e−x/3 from x = 12 to x = 27.

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Q: Set up the definite integral required to find the area of the region between the graph of y = 10 –…

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Q: Approximate the area between f(x) = x+2 and the x-axis from x 1 to x 7 using a trapezoidal sum with…

A: fx=x2+2,  x=1 ,  x=7,  n=3. Here, h=b-an⇒h=7-13⇒h=2 Therefore the subintervals is, 1, 3, 3, 5, 5, 7…

Q: Let f (x) = cos x - sin x for 0 sxs T/3. Find the area A of the region between the graph of fand the…

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Q: Find the area of the region under the graph of f on [a, b]. f(x) = x² - 6x + 13; [−1, 2]

A: To find the area of the region under the graph of f(x)=x2-6x+12 on the interval [-1,2].

Q: 1. Find the area under the curve y a. f(x) = x³ [2,3] b. f(x) = 3√x [1,4] (x) over the stated…

A: a) fx=x3          2,3 b) fx=3x          1,4 Find the area under the curve y=fx over the stated…

Q: Find the area of the region under the curve y = f(x) over the indicated interval. 7 f(x) +3/2 X 2 9

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Q: Set up the definite integral required to find the area of the region between the graph of y = 12 -…

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Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. f(x)…

A: Given. Y = e-3x Area is  dA = e-3xdx Interval is  X>=8

Q: Which of the following represents the area of the region bounded between the graphs of y = +3z and y…

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Q: Find an approximation of the area of the region R under the graph of the function f on the interval…

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Q: Let f(x) = Vx. Set up the definite integral for the area A of the region between the graph of f and…

A: Given function is  fx=x

Q: 7. Find the area of the region under the curve y= |2x – 1| between x= O and x= 2.

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Q: Find the area under the curve y = - - over the interval [4, 9]. (4x + 2)² Enter the exact answer.…

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Q: Use the limit process to find the area of the region between the graph of the function and the…

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Q: Find the area of the region between the curve and the​ x-axis. ​f(x)=36−x2​, from −8 to 8.

A: The function is given by fx = 36-x2;  -8≤x≤8 To evaluate : The area of the region between the curve…

Q: Find the area of the region under the graph of the following function. f(x) 5xe from x = 1 to x = 7

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Q: Find the approximate area under the function f(x)=2.5-2sin(πx/6) using the four middlescribed…

A: From the given picture we see that the middle points are x=1,3,5,7 So we find the x values at these…

Q: (b) Use the midpoint approximation M4 to approximate the area under f(x) = 3x – 2 on [1, 5). Show…

A: a. midpoint approximation

Q: f(x) = x, and g(x) = 3 x 2

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Q: 16. Find the area of the region bounded by the given curve: r = 9eº on the interval ≤0 ≤ 2m.

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Q: find the area of the region under the graph of f on [a,b] f(x) = x^2 -8x +18 ; [-1 , 2 ]

A: The area under the curve is given by:

Q: Let f(x) = Vx. Set up the definite integral for the area A of the region between the graph of f and…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 11 -…

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Q: Find the area under the graph of f(x) = r² + 5 between x = 0 and = 6. %3D

A: The function is given by fx = x2+5 To evaluate: The area under the graph of the function fx between…

Q: Find the area A of the region between the graph of f and the x axis on [-1, 1].

A: Please see the white board for equation formulating the calculation of A.

Q: Which of the following gives the area of the region between the graphs of y =x5 and y = x from x= 0…

A: Graph of given curves will be

Q: Approximate the area under the graph of f(x) = 0.03x* - 1.44x + 43 over the interval [3,7] by…

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Q: If R is the region bounded by the graphs of the functions f(x) = 2 + 5 and g(x) = x + ½ interval [1,…

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Q: 1. Find the area of the region bounded by the curve y = f (x) = |a² – 4| and the lines x = -3, and x…

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Q: Set up the definite integral required to find the area of the region between the graph of y = x- 13…

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Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f(x)…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 20 –-…

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Q: Which of the following gives the area of the region between the graphs of y =x2 and y = -x from x= 0…

A: We have to use area between the curve formula.

Q: Let f (x) = e-* – 1 for 0 sxs 9. Find the area A of the region between the graph of f and the x axis…

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Q: f(x) = e-=/2; [-1,2]

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Q: Area under the curve?

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.