Calculate the area between the graph of f(x) = x² – 36 and the x-axis given x E [-4,6]. 200 а) - 3 800 3 с) 20 760 3 1360 3

Q: Given an area D bounded by a cardioid r = 1 + cos θ, θ ∈ [0, π], x-axis, and it’s located on the…

A: If the curve is given by , where   .The area inside the  curve is  .

Q: Find the area under y = 2x between x = 0 and x= 1 E 3 4. F 3 C H. 1 112

A: To find the area under y=2x from x=0 to x=1

Q: Q4: Find the area bounded by: e) y = 2* , y= x² + 4x and - 4< x< 0.

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Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

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Q: Find the real number b 7 0 so that the area under the graph of y = x3 from 0 to b is equal to 4.

A: The area under the curves y = x3 from x =0 to  x = b is given by integral ∫0bf(x)dx The value of b…

Q: Find the area under y = 3x2 between x = 0 and x = 1 A B. G. H. 31417/4413 1/2 2.

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Q: Find the area between the y-axis and the graph X = 543-2-1 1 2 3 4 5 (y - 3) dy = 6.500 (y - 3) dy =…

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Q: Find the area between the graph of the function and the x-axis over the given interval, if possible.…

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Q: 1) Compute the area between the graphs y = x2 and r = y? for I > 0. 2) Compute the area between the…

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Q: Find an expression for the area between the curves y = x-/2 and y = e between the lines X = 0 and x…

A: In this question we have to find the expression for the area between the curves.

Q: ind the area under the given curve over the indicated interval. 15) y =ex; [1, 2] 4. 3. 2 A) e2 -e…

A: We have to find the area under the curve.

Q: Q2. Find the area between = 0, y = e* and y = e* through the interval [-2,1]. %3D 0.6 0.4 0.2 -2.5…

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Q: d) Find the area under the curve y =f(x) over the stated interval. i) f(x) = x*;[-1,1] ii) f(x) =…

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Q: 1200 1100 1000 900 800 700 600 500 400 300 200 100 100 Find the (exact) area under the curve y = 4x*…

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Q: A Find the area bounded by y = e*, y = xe*² & x = 0.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find the area bounded by the given curve: 16x² +9y² − 64x + 18y-71 = 0 and x² + y² − 4x − 4y+4=0

A: Given the curves, C1:16x2+9y2-64x+18y-71=0C2:x2+y2-4x-4y+4=0. Rewriting, we get…

Q: The area under the curve between z=-1.32 and z=2.12

A: Given information- We have given 2 z-scores and we have to find the area under the curve. To find…

Q: The area under the curve y = 4x bounded by the ines x = 3 and x = 6 above the x – axis O 54.00…

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Q: 9. (a) Calculate the area of the region bounded by the curves y = x² +1 and y = xª between x = 0 and…

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Q: (b) Compute the total area between the curve and the x-axis over the interval [-1,9]. y = f(t) 10…

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Q: The area bounded by the curve x = 3y + 8, the y- axis and the abscissas y = 0 and y = 2 is O 19 O 1…

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Q: rval [1,4] approxim

A: Here we have to find the area between g(x)=ex2 and the x-axis by finding  n = 4 using the left…

Q: 3. Find the area bounded by the curve ay² = r8 and the line * = 4 a. Ans. 142 a².

A: Find the area bounded by the curve.

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: d) Find the area under the curve y = f(x) over the stated interval. i) f(x) = x*;[-1,1] ii) f(x) =…

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Q: S(r) 2 3 4 e 5 Referring to the function above, f(x) dx 0.

A: Given, The graph of function fx  We have to find ∫05fxdx.

Q: (a) Compute f(t)dt. (b) Compute the total area between and the x-axis over the interval YA y = f(t)…

A: We have to find the total area according to the given information

Q: The area between the curves f(x)= x^2,and g(x)=1 1/2 1/4 O 4/3 O 1/3

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Q: The graph shown below is fx) = x + 1. What is the integral function g(t) that defines the area under…

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Q: Find the area under the curve y = e' eº between the linest = 0 and t = 1. 12e + ee None of these ee…

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Q: compute the given approximation to the integral.

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Q: If f(x) = a +2a + 4, then the estimation of the area under the curve y = f(x) between 1 <r < 2 with…

A: We have to choose correct option

Q: ind the area bounded by the curve y²=4x, the lines x=1 and x=4.

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Q: (b) Use the midpoint approximation M4 to approximate the area under f(x) = 3x – 2 on [1, 5). Show…

A: a. midpoint approximation

Q: Q1/A: Evaluate the area under the curve y = -3x2 + 6x + 5 between x = 0 and x = 2

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Q: The area of the region between the graphs of y = x² and y = -x from x = -1 to x = 0 is O is Li (2² +…

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Q: Find the area of the region lying between the x-axis and the curve y = In(7x) – 1 to the right of…

A: Consider the function y=ln7x-1x2. Find region between the curve to the right of line x=e and  x-axis…

Q: Approximate the area under the curve of y = x² + 3 over the interval x = -3 to x = 1 using 4…

A: Recall: Trapezoidal rule  Area=∫abf(x)dx≈∆x2fx0+2fx1+2fx2+···+2fxn-1+fxn where, ∆x=b-a2 We have,…

Q: Q1/A: Evaluate the area under the curve y = x3 + 10 between x = -1 and x = 2.

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Q: 22. Find the area of the shaded region for the function 4e* y = 1+e23 2x

A: The area of shaded region is given by the integral ∫x=ax=b fx dx=∫0ln 34ex1+e2x dx. Let t=ex. This…

Q: Find the area under the curve y = f (x) = Vx; over the x interval [0, 8] 07 12 19

A: Sketch the region

Q: Q2. Find the area between = 0, y = e* and y = e* through the interval [-2,1]. 0.6 0.4 -0.2 -2.5 -2…

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Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = T, using 4 trapezoids.…

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Q: Calculate the area between the graph of f(x) = x² (x + 4) and the x-axis given x E [0, 5].

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Q: | (f(x) – g(x)) dx still equal to the area between the graphs of f and g if f(x) > 0 but g(x) < 0?…

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Q: Find the area between f(x) = 2r ++z+5 and g(a) =+a + 5r +5 between z= -2 and z= 2.

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Q: If P(0 < z < 1.88) = 0.19699, the area under the standard curve which %3D is the left of z = 1.88 is…

A: We have given that P( 0 &lt; z &lt; 1.88 ) = 0.19699

Q: Find b > 0 such that the area between y =x +1 and y = bx + 2 for 0 < x< 3 is

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Q: In item number 5, the integral of Sx3 dx is obtained by applying what Basic Theorem of…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.