Find the area above the curve of -nx and the x-axis. Your knowledge of integrating products may be lound useful. Show all the steps.

Q: Find the area above the curve of - nx and the x-axis. Your knowledge of integrating products may be…

A: To find the area bounded by the curve

Q: Find the exact area between f(x) = 2x and g(x) = 15 – x from the vertical axis to their point of…

A:

Q: Find the area under the curve below from x = 1 to x = 4. y = 5x + (3/x2)

A: We have to solve the area

Q: Evaluate using integration by parts or substitution. 3x dx

A:

Q: Approximate the area under the curve graphed below from 2 = approximation with 3 subdivisions. 1 to…

A: We can solve this using riemann integral

Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum.

A:

Q: Determine whether the following statements is true or false, and explain why.

A: Given integral is: I=∫ln4xdx We have to integrate this function with respect to x.

Q: What is the area under the curve y = x° and above the x-axis between x = 1 and x = 3? What is the…

A: We have to use integration here.

Q: The double integral

A: answer is in step 2

Q: Solve the area bounded by the curve y=5-x^2 and the line y=2x. With graph.

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Q: Use the table method from integration by parts to find: \int (4x^(2)-5x+6)e^(2x)dx

A:

Q: Jxe* dx 3. х se³* dx

A:

Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x-axis, the limits of…

A: Solutions

Q: Find each antiderivative using integration by parts. Do not consult Table 1. 3x dx 3 In x* dx 17.…

A: As per guidelines, we are supposed to solve only first question. Please repost other questions…

Q: Solve for the area beneath the curve y = -(x – 1)² + 10 and above the axis from x = -1 and x = 2.

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Q: Explain the application of integration to area.

A: .

Q: 2. Find the area in the second quadrant bounded by the curve y = x' +4x² –x-4 and the x- axis.

A: To find: The area in the second quadrant bounded by the curve. Given: The equation of the curve is…

Q: Approximate the area between f (x) = x² + 6x + 5 and the x -axis on the interval [0, 2] using 4…

A:

Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: If vertical element is used to find the area bounded by y=/x, x= 4 and the x – axis, the lower and…

A: y=x

Q: Find the area bounded by the curve f(x) = -x² + 10 and the x-axis. Give your answer correct to two…

A:

Q: Find the area included between x2+ y2= 4x and y2= x above x-axis

A: Find the area included between x2+ y2= 4x and y2= x above x-axis

Q: Va2 – 4 dx

A:

Q: Find the total area between y = -x2 - 2x and the x-axis for -3 sxS2.

A: The objective is to find the total area.

Q: 3 +1 dr dy

A: Given integration is  I=∫01∫y1x3+1 dx dy Limits are given y=0 and y=1x=y and x=1

Q: Find the area between the curves. y = x5 - 2 ln (x + 5), y = x3 - 2 ln (x + 5)

A: Given: y=x5-2lnx+5y=x3-2lnx+5

Q: Use integration by parts to evaluate the integral. ∫425 √x lnx dx

A: The integral is given by

Q: The area under the curve y = 2x bounded from below bythe x-axis and on the right by x = 4 is 16 3…

A: Given that the area under the curve y=2xwe need find the area below the x-axis and the right by x=4

Q: Find the area between y = (x - 3) eX and the x-axis from x = 3 and x 9.

A: Give that

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx. Write the given…

A: To find out the value of integral using the midpoint rule.

Q: Write your own definite integral where the total area under the curve is 20.

A:

Q: Sx√x +Tdx

A:

Q: Find the area under the graph of y = 4x + 3, above the x-axis, between x = 1 and x = 4. (You can use…

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Q: Find the area between y=ln(x-6) and y = (ln(x-6))2

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Q: Create table of values and use integration for solving the area.

A: Find the area between the inner and outer ovals of the curve         r2=162-cosθ

Q: The area bounded by the curves: у-х, у-6-х аnd у-0.5х is:

A: see below the answer and explanation

Q: use the table methud from integration by parts to find S(4x2-5x+6e clx

A: we have to find the integral by using integration by parts

Q: Sre* dr

A:

Q: First make a substitution and then use integration by parts to evaluate the integral da

A: Given: The integral is ∫14 8ex dx .

Q: Find the area bounded by y=-17(x2 - x - 12) and the x-axis. Answer in two decimal places.

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Q: Estimate the area under the graph of f(x) = x² + 3x +1 over the interval [1, 3] using four…

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Q: 8) Find the area between the curves: y = x'-9x + 14x and y =-x +9x2 - 14x

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Q: Find the area between the curve and the x-axis over the indicated interval. y = 25 - x2; [-5, 5|

A:

Q: Find the area bounded by the curve f(x) = -x² + 7 and the x-axis. Give your answer correct to two…

A: We have to find Area bounded by the given curve and x-axis.

Q: Evaluate using integration by parts : fln 3x dx

A:

Q: J1/4 Jx2

A:

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: limit of integration

Q: Use integration by parts and find the indefinite integral f(x+2)e dr

A:

Q: Evaluate the integral by reversing the order of integration. 12 3y Ар хр

A: Solution is given below :

Q: -dx x´ +2x+3

A: The given integral,       ∫xx2+2x+3dx

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.