The function f(x) = x2 – 9x + 18 is positive on (0, 3) and (6, 10) and negative on (3, 6). Find the area of the region bounded by f(x), the x-axis, and the vertical lines x = O and x 10. Preview

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A: Given:

Q: Determine the area of the given region. 1. Region between f(x) = x - 3x – 4 and the x-axis from x =-…

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Q: find the area of the region bounded by the functions f(x)=−13x+2 and g(x)=2x−1 over the interval…

A: The given functions are: fx=-13x+2, gx=2x-1 over that interval -2,1 Calculate the area of the region…

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Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

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A: Given curves: The graph is:

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A: We will use rectangle's formula to evaluate the area of curve

Q: Find the area bounded by the ff. curves and lines: a. x^2 - y^2= 9 and y= 2x - 6

A: x2-y2=9  &  y=2x-6 The diagrammatic representation of the area is,

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A: The region is bounded by x=y2 and y=-x2

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A:

Q: Find the total area between the curve of the function f(z) = -4z +8 and the z-axis over the interval…

A: I have provided solution in  step2.

Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

Q: ) Find the area of the region bounded by the lines ( yı=x² ) & (y2=2-x) for x<0.

A:

Q: Find the area of the region enclosed between f(x) = x² +4x + 8 and g(x) = 2x² – 1x + 2. Area = %3D

A: To find the area of the region enclosed between the curves fx=x2+4x+8 and gx=2x2-x+2, first, find…

Q: Find the area bounded by the line f(x)=2x+2, the curve G(x)=X^2-6X +9 and the two vertical lines X=1…

A: Given:       fx=2x+2        gx=x2-6x+9        x=1,x=5 Area bounded by line and curve is:…

Q: Find the area bounded by the ff. curves and lines: a. y = xe^–x , the x-axis and the maximum…

A: To find the are bounded by the curves and lines: (a) y=xe-x, the x-axis and the maximum ordinate.

Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

A:

Q: Find the exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

A:

Q: Find the area of the region bounded by the lines ( y=x2 ) & (y=2+x) for xs 0.

A:

Q: Find the area of the region bounded by f(x) =|x^2−5x+ 6|, the x-axis, and the lines x=1 and x= 4.

A:

Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Find the area of the shaded region  f(x) =8x+2x^2-x^3, g(x) =0

A: f(x) =8x+2x^2-x^3, g(x) =0

Q: Find the area of the region bounded by the parabola f(x) = 16-x^2 and the lines  x=0 and x = 4 and…

A: Givenf(x) = 16-x2lines x=0, x=4 and x-axis(y=20)

Q: Find the area of the region bounded by y = 5-x2, y 2x+2, y=-x-1, a. in terms of x b. in terms of y y…

A: We will find out the required value.

Q: Find the area of the region that is completely bounded by the two curves f(x) = x* g(x) = 3x + 20. -…

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Q: Find the area of the region lying to the right of x = y2 - 5 and to theleft of x = 3 - y2.

A: Given: f(y)=y2-5 and g(y)=3-y2 To find: Where the curve intersect and it is calculated when…

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A: Find the area of the region bounded by y^-x=0 and y^+x=2

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A:

Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

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Q: calculate the area of the bounded figure from the graph of the function y = x²-1 and the axis Ox

A:

Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x–2x²+4y-y² on the region R…

A: The region bounded by the x-axis,y=3x and x=2 is:

Q: Sketch the region bounded by the graphs of the equations f(x) = x5 + 2,      g(x) = x + 2 and find…

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A: Here we will find out the required value

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A:

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A:

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A:

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A: We will find out the area of the region.

Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

A:

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A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

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A:

Q: Consider the region bounded by F(x)=10x3 +7x2 -7x +6 and g(x)= 9x3 +8x2 - x +6. Find the area, in…

A: Given query is to find the area bounded by the curves for the given intererval.

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A:

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A:

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A: Now, from the graph we have the points of intersection of the lines