Suppose that the area under the graph of between 0 and 1 is (x + c)2 8 for some c > 0. What is c? Show working to justify your answer. 15

Q: Find the area under the graph of the function f (x) = xe-* between x 0 and x = 5.

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Q: 1. [0, 3). Find the area between the graph of y = x and the x-axis over the interval

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Q: Find the area under the graph of y = -x² AL 54 3-2 -11° 1 2 3 4 5 X 4x on the interval [-4, -2].

A: We will solve the required.

Q: 6. Compute the area under the graph of f (x) = ! between the vertical lines x = 1 and x = M. Prove…

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Q: Use a finite approximation to estimate the area between the x-axis and the graph of f(x)=2x^5…

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Q: .Find the area under the graph of y = g(x) from -3 to 6, where x², g(x) = 18 – x, x > 2

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Q: Find the area enclosed between f(x)=0.5x2+4 and g(x)=x from x=-4 to x=2.

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Q: Find the area under the graph of f over the interval [3,8). 4x + 5, for xs6 f(x) = - 35 - x, for x>6

A: As per the Guidelines, I can solve only first question. For second question, please post the…

Q: 1. Approximate the area under the graph OF FO)-1+x on [-1,2) USing right endPoints with n=4.

A: We need to approximate the area.   NOTE - SORRY, AS OUR GUIDELINES WE CAN SOLVE ONE QUESTION SO…

Q: Determine the expression for the area under the curve f(x) on the closed interval [0, 3] with n…

A: Definition of the definite Integral

Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

A: Given query is to find the area under the curve.

Q: 2 3. Suppose that the area under the graph of between 0 and 1 is (x + c)² 8 for some c > 0. What is…

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Q: Find the area bounded by x²y = x² - 4 and x-axis, from x = 2 to x = 4.

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Q: 14. Find the area bounded by y = -x² +x + 6 _and y = x2 - x + 2 13

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Q: Find a formula for RN and compute the area under the graph of f(x) = 13x² + 91x over [6, 11] as a…

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Q: Find the area under the graph of g over[-2,3]. (x2 + 4, for xs 0, 3. g(x) 4 - x, for x>0 -x2 + 5,…

A: A function.

Q: Say the function g(x) = ;x + 2. Approximate the area bounded by the graph of y = g(x) and the x axis…

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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: 1. Find the area in the first quadrant bounded by f (x) = 4x - x and the x-axis. %3D

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Q: Compute the area between the x-axis and the graph of f(x)=x(x-1)(x– 2) on [0,3].

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Q: Find the area enclosed between f(x )= 0.8x^2 + 9 and g(x) = x from x = −2 to x = 4

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Q: Use definition to find the area under the graph of f(x) = x² + x and above the x-axis on the…

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Q: 1. Find the area under the graph of f(r) = VI + over the interval [1,2).

A: Integration is used foe determining the area under the graph. Use the given function and domain of…

Q: Find the area under the graph off over the interval [1,4]. x+7, for x ≤2 f(x) = 11-x, for x>2 The…

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Q: Find the area under the graph of f over the interval [1,7]. 6x +5, for xs6 f(x) = 59-3x, for x>6

A: Given

Q: Find the area enclosed between f(x) = 0.3x² + 4 and g(x) = x from x = -3 to x = 4.

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Q: Find the exact area under the graph of f(x) = = and x = 2. Area = 1 x+1 between r=0

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Q: Use the Fundamental Theorem to determine the value of b if the area under the graph of f(x) = 7x…

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Q: 2. ) Find the area below f cx) -x +7x*- 1o x +3 over the interval 1L x<2 (Drow and Illustrate the…

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Q: 8. Find the area bounded by f(x) = (2x² – 9)(2x – 3) on [-2,1].

A: It can be solved using application of integration. To calculate area under a curve f(x), follow…

Q: Find the area enclosed between f(x) = 0.6x² + 3 and g(x) = x from x = -2 to x = 6.

A: Topic:- application of integration

Q: 1. Find the area bounded by the two curves f(x) = x2 - 5 x + 6 g(x) = x + 6

A: Given curves f(x)=x2-5x+6g(x)=x+6

Q: To estimate the area A under the graph f(x) from x-0 to x=4 using n approximating rectangles and…

A: The given function f(x)=1+x3 from x=0 to x=4

Q: Compute the area under f(x)=9x1/2+54x-2 and above the x-axis on the interval from x =1 x=36.

A: Explanation of the answer is as follows

Q: What is the net signed area between f(x)=−2x−6 and the x-axis over the interval [−8,2]? Do not…

A: f(x)=-2x-6 First we graph the given function  Then we look at the intervals to find out the area

Q: Use the Fundamental Theorem to determine the value of b if the area under the graph of f(x)=x2…

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Q: Use the Fundamental Theorem to determine the value of b if the area under the graph of f(x) = 4x…

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Q: Approximate the area under the graph of​ f(x) and above the​ x-axis using n rectangles. f(x)=6/x…

A: The width of the interval [2, 10] is = 10-2=8 There are 4 partitions. So the width of each…

Q: 3. Find the area between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x = 1

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Q: 9) Given the function f(x)=-x+4 , find the net signed area between f (x) and the x-axis over the…

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Q: Find the area of the region under the graph of f(x) = In(x) from x = 7 to x 14.

A: Here we find the area of the region under the graph of f(x)=ln(x) from x=7 to x= 14 so, we use…

Q: (A) Estimate the area under the graph of 3 f(x) = from x = 1 to x = 5 using 4 approximating…

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Q: c) [1 graph of : Estimate the area under the f(x) = x² + 1 from x = 0 to x = 2 using four…

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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: 13. Find the area bounded by y = -x + 3 and x = 9- y2 13

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Q: 5. Find the area bounded by the graphs of f(x) = x2 – 3x – 10 and g(x) = x + 2 %3D -

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Q: Which of the following represents the area bounded by the graphs of f(x) = −x3 + 12x and g(x) = x2

A: Definition used-       The area between two curves f(x) and g(x) is given by -             A…

Q: 2. Find the area bounded by y = 4x – x² and the x – axis. · Solve in two ways.

A: Solution:Giveny=4x-x2   and x-axisTo find the area of the bounded region.Formula:Area=∫abydx

Q: Compute the area under the curve of f(x)= e4 1 from x = 2 to x = 5

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Q: Let f(x) be defined by the following graph. Estimate the area under the graph of f(x) using…

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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.