Example: When does Sa f(x) – g(x) dx compute the area between the graphs of f and g between on the interval [a, b]? Give an example where the integral computes the area.

Q: 1. Express the area bounded by the graph of g(x) and the x-axis as an integral on the interval (-00,…

A: Double integral is used to integrate the function of two variable over two-dimensional region.…

Q: Determine the area bounded by x²=y-1 and x=y-3

A: To find: The area bounded by the region x2=y-1 and x=y-3. Formula used: The area under the curve…

Q: a) Using a Riemann sum with right endpoints and n = 4 subintervals, estimate the area under the…

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Q: Let A be the area of the region that lies under the graph of f(x) =e -x  between x =0 and x =2

A: The diagrammatic representation of the area is,

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 bounded by x²y = x² - 4 and x-axis, from x = 2 to x = 4.

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Q: 4. Set up the integrals to find the area bounded by f (x) = 3x³ – x² – 10x and g(x) = -x² + 2x. %3D

A: To determine: The integral which represents the area bounded by given functions.

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

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Q: 7. Let f(x) = x² + 1 and g(x) = 2x + 9. .) Set up the integral to find the area of the region…

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Q: An approximation of the area under f (x) = x² , using right endpoints on [0,1] and n =4 is: %3D

A: For the given curve f(x) = X2 under the interval [0,1] and n= 4  approximation area under the curve…

Q: Use integration to find the area bounded by g(x) = 3x + 4 – x², x = 1, 0 0. (b) Write the first…

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Q: find the area between f(x)=x2+2 and g(x)=-x+1 on [1,3]

A: Draw the graph. To find the region between the red and blue function: Red: y=x2+2 Blue: y=-x+1…

Q: d the area bounded by the graphs of x = y² and x 2 - y²

A: Topic = Area

Q: Find the area enclosed between f(x) = 0.65x² + 7 and g(x) = x, on the interval from x = -3 to x = 5.

A: Given,  fx = 0.65x2+7 gx = x  We have to find the area enclosed between fx and gx on the interval…

Q: Find the area between f(X)= -x2+4x and g(X)=x2-6x+5 over the interval 0 ≤x≤ 1. sketch the region

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Q: Express the area bounded by the graph of g(x) and the x-axis as an integral on the interval [0, 10]…

A: The area between the curves can be calculated using integration. The integrand for the integration…

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: Express the area bounded by the graph of g(x) and the x-axds as an integral on the interval (-, ) in…

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Q: B) Compute the area under the curve of the function f(x) = x(3x – Vã), between x = 1 and x = 4.

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Q: i attached the problem below.  Thank you! :)

A: Find the area bounded by curves

Q: 11. Set up and evaluate integral to find the area of the region bounded between the x-axis and the…

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Q: Find a formula for the area function of f (x) = 2x + 4 with lower limit a = 0.

A: Integrals and derivatives are considered to be inverses of each other. For example if we integrate a…

Q: 2. Find the area under the curve y = x² from x = 0 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

A: Solved below.

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: Find the area bounded by the graphs of y = cos x and y = x² y=x² y = cos x + X

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Q: Find the area enclosed between f(x)=0.5x2+8 and g(x)=x from x=-2 to x=2.

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Q: compute the area of the region under f(x)= ln x over the interval (1,e)

A: The solution is given by using the formula for area under the curve

Q: Use the Riemann Sum to find the area for the region bounded by the graph of f(x)= 2x+3x^2 and the…

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Q: (6) Set up (do not solve) a definite integral to compute the area of the region between the graphs…

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Q: 1. Let f(x) = x? Using the rectangle sum method, estimate the area under the curve for the interval…

A: Given the functionf(x)=x2

Q: Use the Fundamental Theorem of Calculus, Part I to find the area of the region under the graph of…

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Q: Use finite approximation to estimate the area under the graph of f(x) = 2x³ and above the graph of…

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

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Q: Find the area bounded by f(x) = -x² +4x +1 and g(x) =x+1

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Q: Use the Fundamental Theorem of Calculus, Part I to find the area of the region under the graph of…

A: As we know that the fundamental theorem of the calculus; If dFxdx=fx, then ∫abfxdx=Fxab=Fb-Fa.…

Q: b) Find the area enclosed between f(x)= = -x² + 4x and g(x) = x² - 6x + 5, over the interval 0≤x≤ 1.

A: Sol

Q: The right-endpoint approximation of the area under the curve of f(x) = x² over the interval [0, 2]…

A: fx=x2 over the interval 0,2 for n=4

Q: Use Riemann Sum to find the area bounded by f(x) and the x – axis: f(x) = 4 – x² over [-2,2] x =…

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Q: Find the area under the graph of y = g(x) from -2 to 5, where x³, 4 – x, x 1 -

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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: 22. Sketch the region bounded by f(x) = Vx -1 and g (x)=x-1 AND find the area.

A: Sketch

Q: Find the area A of the region between the graphs of f and g on the interval [1/2, 2]

A: It is given that fx=1x,gx=1x2 and the interval is 12,2. Recall the fact that the area of two curves…

Q: Find the area under the graph of f over the interval [-2,4]. .2 X+6 XS2 f(x) = %3D 5x x> 2

A: To find the area under the graph of the function fx over the interval -2, 4.fx=x2+6,   x≤25x,…

Q: Find the area between f(x) = x - 1 and g(x) = -x² + 6x - 5 %3D

A: We have been given the graphs f(x)=x-1g(x)=-x2+6x-5

Q: Express the area bounded by the graph of g(x) and thex-axis as an integral on the interval (-00, 00)…

A: We need to express the area bounded by the graph of gx and the x-axis as an integral on the interval…

Q: 7. Let f(x) = x2 +1 and g(x) = 2x + 9. .) Set up the integral to find the area of the region bounded…

A: To find the area bounded by the curves

Q: Use the Fundamental Theorem of Calculus, Part I to find the area of the region under the graph of…

A: Given curve:- y=4cosx   To find:- Area under graph on [0, π/6]

Q: Exercise 9. Find the area bounded by the graphs of functions y = x°, y = 8, x = -1.

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Q: Write a definite integral that represents the area of the region. y1 = x2 y2 = x3

A: The equations for the two curves are as, y1=x2y2=x3 Finding the point of intersection of the curves,…

Q: Express the area bounded by the graph of g(x) and the x-axis as an integral on the interval [0, 10]…

A: Let us consider a function f(x)  defined on the interval [a,c)∪(c,b] then the integral defined as…