Find the area the region lying between the x axis and the curve y=(ln(8x)-1)/x2 to the right of the line x=e

Q: Find the area between the curve y = -x< + 6x – 8 and the x-axis from x = 2 to x = 4. (Give an exact…

A:

Q: Estimate x dx using midpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: we have to estimate ∫03x2dx using midpoints for n=4 approximating rectangles.

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

A:

Q: 3 Estimate x dx using right endpoints for n = 4 approximating rectangles. x² dx is approximately

A:

Q: Find the exact value of the area between the graphs of e for 0 < x < 1.9. y = 1 – x and y area =

A: Recall: Area=∫abf(x)-g(x)dx We have, a=0, b=1.9, f(x)=1-x, g(x)=ex

Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₂ = x + 2…

A:

Q: Estimate the area under the graph of f(x) 1 over the interval [2, 6] using eight approximating x2 +…

A: A function is given by, fx = 1x2+4 over the interval 2,6. The objective is to find the area under…

Q: use a definite intergal to find the area under the curve between the give x-values. f(x)=2ex from…

A: Given data: f(x)=2ex from x=0 to x=ln4

Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

Q: Find the area of the region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and…

A: The region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and x = 2 is as…

Q: Estimate the area under the graph of f(x) 1 over the interval [0, 4] using eight approximating x + 4…

A: Given fx=1x+4. To find the area of f(x) over the interval [0,4].  Here, a=0 and b=4. Number of…

Q: Find the area enclosed by the given curves. 11) Find the area between the curve y = 6x/(1 + x2) and…

A:

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

A:

Q: 1 Estimate the area under the graph of f(x) : x2 + 4 over the interval [- 1, 3] using ten…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) arcsec(7x) dx, x >

A: We need to find the indefinite integral.       ∫arcsec7x dx,    x&gt;17

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: Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

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: 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 between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: Approximate the area under the curve graphed below from x=2 to x = 6 using a Left Endpoint…

A:

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

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

A:

Q: Estimate the area under the graph of f(x) = 3x2 18x + 28 over the interval [0, 6] using five…

A:

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: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Consider the provided curve,  Bounded above by the curve y=ex2 and below by the curve y=e-x2. And on…

Q: 22) Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2 sxs2 of the…

A:

Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

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

Q: Estimate the area under the graph of f(x) : 1 over the interval [0, 4] using five approximating x +1…

A:

Q: Estimate the area under the graph of f(x) 1 over the interval [– 1, 4] using ten approximating x + 4…

A:

Q: Estimate the area under the graph of f(x) = 1 over the interval [0, 5] using eight x + 2…

A:

Q: Estimate (2x – 5) dx using midpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: 4

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

A:

Q: Graph the function y = -0.3x² + 1.5x over the interval [0, 6]. (0, 6] by (-2.25, 2.25] a. Integrate…

A: Given function y = - 0.3x ^ 2 + 1.5x over the interval [0, 6].   To find  a. Integrate y = - 0.3x ^…

Q: Estimate the area under the graph of f(x) = rectangles and right endpoints. Rn = Repeat the…

A:

Q: Estimate the area under the graph of f(x) : 1 over the interval [- 1, 1] using ten approximating…

A:

Q: 7. Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line p through the…

A:

Q: Estimate the area under the graph of f(x) = x² – 2x + 5 over the interval [0, 7] using ten…

A:

Q: Find the areas between the curves y = 2(log2 x)/x and y = 2(log4 x)/x and the x-axis from x = 1 to x…

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

Q: Find the area bounded by y = 0.5(x- 2)² – 1 and the X-axis from x-3 to x-5. Show the sketch with…

A: y= 0.5(x-2)2-10 =0.5(x-2)2-11 = 0.5 (x-2)22 = (x-2)2x - 2 = ± 2x =2+2    x~ 3.414orx =2-2x ~ 0.586

Q: Estimate the area under the graph of f(x) 1 over the interval x² + 2 rectangles and right endpoints.…

A:

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

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: Estimate the area under the graph of f(x)=1/ x+2 over the interval [3,8]using ten approximating…

A: We need to find area.

Q: What is the slope of the curve y = ex at x = ln 2? What is the area of the region bounded bythe…

A: Consider the curves, y=ex,x=ln2 Differentiating with respect to “x” then, dydx=ddxex=exTo  calculate…

Q: 2 Find the area between the curves y= 2x +6x+1 and y =-x +3x+7 over the interval [-4,10]. Draw the…

A:

Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

A:

Q: Find the most general antiderivative or indefinite integral. 8/x dx

A: We have to find the indefinite 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.