Evaluate the area of the unbounded region between the graph of y = e^−x? and the x −axis over the interval [1, ∞).

Q: Find the area between = 0, y = e-* and y = e* through the interval [-2,1]. 0.8 0.6 0.4 0.2 -2.5 -2…

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Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

A:

Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

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=…

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Q: Find the area between the graphs of y=8x-x+7 and y 3x -x+ 12

A: The given problem is to find the area between the given graphs. Given functions y=8x2-x+7 and…

Q: Find each of the two areas bounded by the curve y = x³ – 4x and y = x² + 2x. Solve in two ways.

A: Given curves are, and Comparing both,

Q: calculate M6 for f(x)=7(In(x^2)) over [1,2]

A: Given the function f(x) :

Q: Find the area between the curve y = sec (4x) and the line joining the points (-,2) and (. 2).

A: Consider the given information: To find the area between the curve and the line joining the points.

Q: Find the area under the graph of f(x) = x² + 10 between x = 0 and x = Area = 6.

A: Givenf(x) = x² + 10x = 0 & x = 6

Q: Find the total area between the x-axis and the curve f(x)= = x = 1 and x = 9. O a.) (10ln5-5ln9)…

A:

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.