1) Suppose F is an antiderivative of f and A is an area function of f. What is the relationship between f and A? What is the relationship between F and A?

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

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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: 9. Find the area between y = √x and y = √x+1, over the interval 0≤x ≤4

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Q: 1. Find the area between the curve f(x)=√x and g(x) = x³.

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Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area

Q: 1. Find the area bounded by the curve y In x and the %3D lines y = 0 and x = e.

A: Given curve is: y=lnx and the line y=0 and x=e Area of bounded regions: Let y=f(x) be a continuous…

Q: - 4. Find the area bounded by y = x - x² and y = x(x − 2)(x+2).

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Q: 1. Determine the area under the curve y = x² + 5 from xX1 = 0 to x2 = 1.

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Q: 2. Find the area bounded by y = x² - 2 and y = 2x + 1.

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Q: 8. Find the area bounded by x² – 6x + y = 0, x² – 2x – y = 0, and the x – axis.

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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: 2. Determine the area under the curve y = on [0, 1].

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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: 2 6) Compute the area bounded by y² + 2y + 4 and y = 4.

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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 under the curve over the indicated interval. 5. y = x - x2; (0, 1] 6. у 3 [1, 3]

A: y = x-x2 ; [0, 1] y = 4/x; [1, 3]

Q: Suppose F is an antiderivative of f and A is an area function of f. What is the relationship between…

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Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

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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: 3. The following curves bounds a certain area: y = 4x – x² y = 4 and x = -2 Determine that area.

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

A: I am attaching image so that you understand each and every step.

Q: 3 8) Find the area bounded by y = x = 0, y = 0, and x = 2. Vs1 - 9x2

A: Given function  y=381-9x2 y=39(9-x2)y=339-x2y=19-x2 To find area bounded by the curve

Q: 7) Determine the area bounded by the x-axis under the line y = 2x+1 from x=1 to x=4

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Q: 7 Find the area under the curve y = x over the interval [1, 5]

A: Please refer to the image below

Q: Compute for the area between z = ±1.43.

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Q: 1. Find the area bounded by y = -x' - 3x and y =- 4. |

A: solve the following

Q: 2. Find the area between between x = 0 and x =9. y=√x-10 and y=0 10

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Q: 14. Determine the area bounded by x = 1, x = 2, and y = e*.

A: To solve this problem, the function y needs to be integrated from x=1 to x=2

Q: 6. Compute the area enclosed by the curves y = x² - 9 and y = 9-x2. Page 5

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Q: x* = 9-y and x*= By By

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Q: 12 Find the area under the curve y = over the interval [ – 1, 1]. (x + 2)² area = i

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Q: The area between y 3 x + 1 and y x2 from x = 1 to x 3 is

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Q: 1. Find the area bounded by: x=y² and y=-x².

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Q: (1) Find the area enclosed by the two functions f(x) = x² – 1, and g(x) : -x4 + 1.

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Q: Let a be the number such that the area to the right of z=a is 0.21  Without using tables or…

A: The normal distribution:A continuous random variable X is said to follow normal distribution with…

Q: 3.) Find the area under the curve j(x)= 6. V3 to x = 1 from x = %3D VI- x2

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Q: 11. Evaluate the area under the curve y= on the interval [7, 9].

A: Given,            The curve is y=x2 and the interval is 7,9.To find : Evaluate the area under the…

Q: In your own word define how do you find area under function f(x) for x=a to x=b

A: To define area under function f(x) for x = a to x = b

Q: х — 18 Find the area bounded by Y x = 5, x = 6, and y = 0. г? — 5а — 24 -

A: To determine the area bounded by the given curve.

Q: Compute the area under the curve of f(x)=e^4x − 1/x from x=2 to x=5

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

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Q: Find the area under the curve from z = −1.5 to z = 2

A: Suppose the area under the curve from z = −1.5 to z = 2 is A. P(-1.5 < Z < 2)  = A

Q: Find the area between  F(x) = x^2-5 and the x-axis from x=0 and x=9

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

Q: 9) Find the area bounded under the curve y = x+2 and y=x² – 4.

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Q: Find the area under the curve  over the stated interval. fx=x^-2/3;[1,27]

A: Area under the curve f(x) between the interval [a,b] is given by:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.