Set up but do not evaluate an integral that would be used to find the area enclosed by the curves f(x) =-x² – 2x² + 5x –1and g(x)=-5x+2. Include a sketch with the enclosed area shaded. You may use your calculator to assist you with the curves. a. Sketch b. Integral

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Evaluate the integral. NOTE: Enter the exact answer. + 13/x| dx +C [ 20:r3

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x²e-9r³ dx +C

A: ∫x3e-x3dx

Q: Find the area between the x-axis and the function y = x2 - x - 2 over the interval [-1,4]. Round to…

A:

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Given y=49−x2−5≤x≤5

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: O Find the integral f xsec2x dx

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Q: Xy =1 y=x, x-2 , y=0

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Q: Which of the following is the correct integral setup to find the area enclosed by the curves f(x) =…

A: Consider two curves, f(x)=2-2x and g(x)=x2-1 f(x) is straight line , to plot f(x) consider x 0 1…

Q: 1. f(x)=x²+2x+1 & f(x) = 2x+5

A: To find the area between the curve.

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

A:

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Given:     y = √(64-x2)    -7 ≤ x ≤ 7

Q: Using iterated integrals, graph and find the area between the parabolas y2 = 4ax and x2 = 4ay.

A: GIVEN - TWO PARABOLAS ARE GIVEN y2=4ax and x2=4ay TO FIND- AREA BETWEEN 2 PARABOLAS CONCEPT USED-…

Q: Write a definite integral that represents the area of the region.                        g( y) = y3

A: Given  g(y)=y3

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (7x – 6)° dx…

A: To evaluate the integral ∫7x-69dxFormula:∫xkdx=xk+1k+1+C

Q: Evaluate the integral.

A:

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Given:    y=25−x2,  −1≤x≤1.

Q: Q2. Find the area enclosed by the curve y = x³ – 3x² + 2x and the x-axis.

A: To find the area enclosed byy=x3-3x2+2x and x-axis

Q: Sketch the graph and set up the integral of the area of: a). Inside r1, but outside r2 b). Inside…

A:

Q: Write a definite integral that represents the area of the region.                        f(x) =…

A: Given: fx=4x2+2 for find shaded area A region we integrate given function in interval -1 to 1

Q: Use substitution to find the indefinite integral. p(p+3)°dp

A:

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Given that:-y=81-x2 ,      -8≤x≤8To find : Surface area of revolution about the…

Q: Find the area bounded by the curves x² + y? – 2x – 24 = 0 y2 – 8x + 16 = 0

A: The area between two curves y1 and y2 such that y2>y1 between the limits x=a to x=b is given by;…

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Given: y=36-x2, -5≤x≤5

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 8 dx +C –…

A:

Q: Write a definite integral that represents the area of the region.                      f(x) = 4 −…

A: Given: fx=4-x,   -4≤x≤4

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Set up, but do not solve, a definite integral that represents the accumulation of the shaded region…

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 4x²e" dx = +C

A: Given:          ∫4x2ex3dx         =4∫x2ex3dx substitute u=x3→dudx=3x2                     dx=13x2du…

Q: The area bounded by the curve y = 6x , the x-axis and the ordinates x = = 0, x = 2 is 6 O 3 O 12 O…

A: area bounded by curve and x axis given by integrating curve

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) xp…

A: The given integral is x/(x4+10x2+26).

Q: The area which is enclosed by the curve x2 – 10x + 4y + y? = 196 is O 12n 15n О 14п 144n O 225n

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Q: SET UP the definite integral that will give the area of the shaded region (as shown below) using a.…

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Q: Evaluate the integrals. Simplify your answers. dx J4/3 4x+vx³

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Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) xp…

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. dx 4 +C (2 –…

A: Substitute the denominator and simplify then integrate.

Q: Find the area under the curve of the parabola y = x? - 2x + 2, above the x-axis and between x=0 and…

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Q: Write a definite integral that represents the area of the region. Y1= 3(x^3- x) Y2 = 0

A: The given equation is y1=3x3-x, y2=0. Find the definite integral that represents the area of the…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 4 dx = +C (1…

A: Given:         ∫41-2x6dx     =4∫11-2x6dx substitute u=1-2x→dudx=-2             dx=-12du…

Q: SET UP the definite integral that will give the area of the shaded region (as shown below) using a.…

A:

Q: Find the area enclosed by the line x = y+ 1 and the parabola y = 2x + 6. All answers must be in…

A: Given curves are  x=y+1y2=2x+6

Q: Using iterated integrals, find the smaller area cut form the circle x² + y2 = 16 and the line y =-1.

A: to find the area we consider th strip parallel to y axis  and desctribed the region as below

Q: Use geometric interpretation of a definite integral to com- pute f, V25 - r²dx and f,"5dx. Draw the…

A: To find the solution

Q: (x² + y²)dx + 2xydy where C It's the curve y = x³ from x = 0 to x = 1

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Q: Use the technique of completing the square to evaluate the following integrals. x- 6x Show your…

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Q: Find the area bounded by the curve y=x^2, the axis, and the ordinates are x=1 and x=3.

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Q: Write a definite integral that represents the area of the region. f(x) = tan x

A: To Determine: Write a definite integral that represents the area of the region. f(x) = tan x Given:…

Q: Set up, but do not evaluate, an integral for the length of the curve. xex⁹ Jo y = 0≤x≤5 dx

A: Given,  y=xex9, 0≤x≤5

Q: Use substitution to find the indefinite integral. P(p + 9)°dp

A: We have to find given integral.

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.