Let f(x)=9-x^2 Consider the region under the graph on [0,3] and bounded by the x-axis. Divide this region into 6 subintervals and compute an estimate of the area using left endpoints for each partition.

Q: Compute the area of the region enclosed by graphs of the functions y=x^3−2x^2+x and y=x^2−1x…

A: From the definition of area between two curves, say f(x) and g(x) in the interval [a, b], we have…

Q: Approximate the area under the curve of y = -+x+5 over the interval x = -1 to x = 4 using 5…

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Q: Set up an integral representation for the area of the region bounded by y=-x^2  and  y=-x-2

A: Given y=-x2 and y=-x-2

Q: Find the area under the graph of f(x)=4-x2  on the interval[-1,2]

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Q: Find the area of the region bounded by the graph of f(x) = x² + 1, the x-axis and the vertical lines…

A: Explanation of the answer is as follows

Q: Estimate the area under the graph of f(x)=√x+2 over the interval [ - 2, 0] using eight approximating…

A: To estimate the area under the graph of fx=x+2 over the interval -2, 0 by using eight approximating…

Q: Estimate the area under the graph of y = 2° for x between and 2. Use a partition that consists of 4…

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Q: 5. Find the area of the region bounded by f(x) = -x? – 2x + 3, x-axis, and interval [0, 2].

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Q: Sketch the region bounded by the graphs of the following functions and find the area of the region.…

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Q: Find the area under the graph of x = 4 - y² on the interval [0, 2]. -3 -2 -1 1 2 3 → 1 0 -1 16 3 16…

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Q: Find the area of the region bounded by the graphs of f(x)=x^(3)+2x^(2)-3x and g(x)=x^(2)+3x

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Q: Find the area of the region R bounded bythe graph of ƒ and the x-axis on the given interval. Graph ƒ…

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Q: Evaluate the area of the region bounded by x=y^2 and y^2 = 6-x

A: To find the area

Q: Determine the area of the region bounded by the curves y = x4 - x2 and y = x2 - 1

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Q: Estimate the area under the graph of y = x2 + 2x for x between 0 and 2. Use a partition that…

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Q: . Determine the Total Area bounded by f(x) = x´ – 1 on the interval [- 2,2].

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Q: Estimate the area under the graph of f(x) = Vx + 1 over the interval [– 1, 15] using eight…

A: (1) To find the area under the graph fx=x+1 over the interval -1,15 using midpoint formula where…

Q: Estimate the area under the graph of f(x)=x^2+4x from x=1 to x=5 using 4 approximating rectangles…

A: The given graph of the function is f (x) = x^2+4x from x = 1 to x = 5.The number of triangles is…

Q: Use finite approximations to estimate the area under the graph of the function f(x)=3−x2−2x between…

A: The Given function is, f(x)=3-x2-2x  Between x=-3 and x=1 Here we have to find the area under the…

Q: Compute the area of the region enclosed by y=3-2x-x2   and the x-axis.

A: First we find the points where it cuts the x-axis. For this, solve the given curve by equating it to…

Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) = sin…

A: Solution -  Given function is - f(x) = sinxWe have to calculate the area enclosed by f(x) from x =…

Q: Find the area of the region bounded by the graphs of f(x) = 5 − x^2 and g(x) = x^2 − 3

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Q: Find the area of region bounded byf (x) = 8 – x², g(x) = 2x , from x = 0 and x = 2. Show all work.

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: 4. Find the area of the region bounded by f(x) = (x + 8)(x + 2)(x - 6), x axis, and the interval…

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Q: Estimate the area under the graph of f(x) = x° between x = 0 and x= 4 using each finite…

A: Given: f(x)=x3   between x=0 and x-4

Q: Find the exact area of the region bounded by the x-axis and the graph of y = x - x. Area =

A: Solve for area

Q: 1. Determine the area of the region bounded by y = x+2 , y = 3 (x + 2)²,x = -,x = 1.

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Q: Find the area of the region bounded by f(x) = -x² – 2x + 3, x-axis, and interval [0, 2].

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Q: Find the area of the region under the graph of f (x) over the interval (1,8).

A: Given: fx=12x23; x∈1,8 for finding area of the region under the graph of given function on given…

Q: Find the area under the graph of f(x) = 4-x² on the interval [-2, 1].

A: The given function is f(x)=4-x2 and the interval is -2,1. Draw the graph of the function f(x)=4-x2.

Q: Use left endpoints and 6 rectangles to find the approximation of the area of the region between the…

A: Let's find.

Q: determine the area of the region bounded by x= |y| and x=2-y2

A: determine the area of the region bounded by x= |y| and x=2-y2

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

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Q: Find the area of the region under the graph of the function f on the interval [1, 4]. f(x) = 5Vx…

A: The function is given by fx = 5x To evaluate : The area of the region under the graph of the…

Q: find the area of the region under the graph of the function f on the interval [0,3] f(x) = 3x-x^2

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Q: Find the area of the region bounded by the graph of f(x) = x(x + 2)(x - 1) and the x-axis on the…

A: Area of the region bounded by f(x) and x- axis

Q: Sketch the graph of the region enclosed by y = 4 – x² and y = -x+2 and calculate its area.

A: From the given curve bounded region is shown below:     Now finding the point of intersection:…

Q: How do I solve this problem?

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Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) = x3…

A: Given function f(x) -f(x) = x3-1Intervals = -1, 2Let's first draw the curve of f(x) over the given…

Q: Find the area of the region R bounded bythe graph of ƒ and the x-axis on the given interval. Graph ƒ…

A: Consider the given function as fx=1-x2-12

Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) =1/x…

A: To Find  The area of the region bounded by thegraph of ƒ and the x-axis(y=0) on the given…

Q: 17) Find the area of the region bounded by the graphs of y = 3x² and y = 12.- %3D

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Q: Find the area of the region bounded by the graphs of f(x) = -x² + 2x +5 and g(x) = |2x|.

A: Here we have to find out the area bounded by the given curves.

Q: Find the area of the region bounded by the graphs of x = 3-y^2 and x = y+1

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Q: Compute the area of the region bounded by the curves f(x)=1/x+2,g(x)=(x+2)^2 and the lines x=-3/2…

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Q: Find the area of the region bounded by the graphs of f(x)=5-x^2 and g(x)=x^2-3.

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Q: What is the area of the region between the graphs of y = x3 and y = -x from x = 0 to x = 2

A: Area between curves

Q: Compute the area of the region bounded by thegraph of ƒ and the x-axis on the given interval. You…

A: Given,f(x) = x3 - x on [-1, 0]

Q: Estimate the area under the graph of f(x)=√x+3 over the interval [−3,1] using eight approximating…

A: Given :  Function f(x) = √(x+3), Interval [-3,1], To find : Area under the graph of given function…

Q: Estimate the area under the graph of f(x) = 16 – x² over the interval [– 1, 4] using ten…

A: RIGHT HAND SUM Consider the following variable, n=number of rectangles∆x=width of each…

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.