Calculate the area, in square units, bounded by g(x)=4x−2 and f(x)=5x−15 over the interval [−11,4]. Do not include any units in your answer.

Q: Evaluate the integral.

A: Given integral is We will use the following substitution to evaluate the integral.

Q: Calculate the area, in square units, bounded by g(x)=5x+19 and f(x)=x2 +x−41 over the interval…

A: The given functions are f(x) = x2+x –41 and g(x) = 5x+19 over the interval [–6,10].

Q: Evaluate the integral. x°V1- x2 dx

A:

Q: find the integral of F(x) = x6(x7-8)4 dx

A:

Q: Calculate the area, in square units, bounded above by f(x)=x2+8x+16 and g(x)=8x+80 and bounded below…

A: The solution of the problem is given in the next steps.

Q: Calculate the area, in square units, bounded above by f(x)=x2+4x+4 and g(x)=−4x+4 and bounded below…

A: Consider the curves, fx=x2+4x+4,   gx=-4x+4 To sketch the graph: Here there are two region be…

Q: Find the area bounded by the line f(x) equals 3X -1, the curve G(x) equals X^2-6X +7 , and the two…

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Q: Evaluate the integral. (Use C for the constant of integration.) x3 xp 49 + x2

A: In this we have to solve by putting the value of u=49+x^2 I'm providing hand written solution for…

Q: Find the volume of the solid formed by rotating the function around the x-axis in the range 0≤x≤1.

A:

Q: Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 6. ...

A:

Q: Consider the function f(x) = x² - 3x + 2 on [0,4], Find the total area between the curve and the…

A:

Q: 3. Find the exact area between the curve f (x) = -2x² + 12x + 7, the x-axis, and x=1 and x=5.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Consider the region bounded by g(x)=7x−6 and f(x)=x2+19x+14. Find the area, in square units, between…

A: The given two curves that bounds a region is,

Q: Find the area between the curves f(x) = −x² + 4x and g(x) = x² - 6x + 8.

A: Basic identities of integration are used

Q: Find the area bounded by f(x) = 4x − x2 and the x-axis. (In square units)

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

Q: Use substitution to find the indefinite integral

A: Given, ∫2+lnxx dx

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 under the graph of f(x) = 3x2, above the x-axis, and between x = 0 and x = 2.

A:

Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

A:

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: Calculate the area, in square units, bounded by g(x)=4x+8 and f(x)=x2 +19x+62 over the interval…

A: We have to find area between f(x) and g(x) for given boundaries.f(x) and g(x) is given below:Graph…

Q: x° + x dx Vx3

A:

Q: Find the area between the curve f(x)=x^3−110 and the​ x-axis from x=1 to x=3.

A:

Q: Find the area of f(x) = 3 +2x – x² above the x-axis.

A:

Q: Find the area between the curve y = x2 + 10x + 16 and the x-axis from x = −2 to x = 1.

A: We have limits of curve from x=-2 to x=1

Q: Calculate the area, in square units, bounded by g(x)=4x+8 and f(x)=x2+19x+62 over the interval…

A: The area enclosed by the parabola and line is given by

Q: valuate the integral ∫x2/x3+1dx using an appropriate substitution.

A:

Q: 5) Calculate the area in square units, bounded by g(x)= 4x+8_and_f(x)=x² +19x+62 over the interval…

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the interval is  so…

Q: Find the area of the region between the curve and the​ x-axis. ​f(x)=36−x2​, from −8 to 8.

A: The function is given by fx = 36-x2;  -8≤x≤8 To evaluate : The area of the region between the curve…

Q: Sx³(a² + x²)î dx

A: We will solve the problem.

Q: Calculate the area between the curves: f(x) = x² + 31 and g(æ) = x + 73 over the interval of – 6 < x…

A: fx=x2+31 &amp; gx=x+73 The diagrammatic representation of the area is,

Q: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

A: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

Q: Find the area (in square units) of the region under the graph of the function fon the interval [-1,…

A:

Q: Write a definite integral that represents the area of the region. y1 = x2 + 2x + 1 y2 = 2x + 5

A: The given equations of the curves are: y1 = x^2 + 2x + 1 y2 = 2x + 5 At the points of intersection…

Q: Find the area above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

Q: Find the area between the curves, f(x) = ;x² and g(x) : - x over the interval [0, 2] 10 3 - 1/3 2.

A: We first sketch the region

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Find the total area between the function f(x)=3x+8 and the x-axis over the interval (−4,−1). Submit…

A: To calculate the unsigned (total area) of the region: in calculating total area, we take only the…

Q: find the area between the curves: f(x) = x2  + 1,   g(x) = 3 - x   on the interval [0,3]

A:

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

A:

Q: Given the function f(x)=−x−2, find the total area between f(x) and the x-axis over the interval…

A: To find the area of the given region which may lie both above and below the x-axis.

Q: Find the total area between the curve of the function f(x)=−2x and the x-axis over the interval…

A:

Q: Find the area between the curve f(x) = −3x^2 + 3 and the x-axis over the interval [−1, 2].

A: Answer and explanation is given below

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

A: The given two curves:fx=x2-8x+8 and gx=-x2+6x-8and the two vertical lines are x=3 and x=4.We need to…

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 9 -x, and the line perpendicular…

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Q: Evaluate the integral: x2 dx V1 - x6

A: Given integral is: ∫x21-x6.dx

Q: Find the area bounded by the line f(x) = 3x - 5, the curve g(x) = x² – 10x + 7, and the two vertical…

A:

Q: Sx (x² + 4)5 Se3*dx

A:

Q: Consider the region bounded by f(x)=−x2+11x−3 and g(x)=5x+5. Find the area, in square units, between…

A: Given:

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.