The area of the region in the first quadrant bounded below by the curve y=e* and above by the curve y=e and on the right by the line x-Ln (3) equals

Q: 1. Use a suitable substitution to evaluate , (G) dx. Give you answer correct to at least 2 decimal…

A: Substitution is done for the function whose derivative is present in the numerator.

Q: The rate at which a substance grows is given by R'(x) = 200 e0.5x, where x is the time (in days).…

A: The given growth rate is, R'x=200e0.5x. Here, x is the time in days. The object is to find the…

Q: A hemisphere-shaped dome of radius 75 ft is to be coated with a layer of rust-proofer before…

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Q: 38. Use numerical integration to estimate the value of dx. п

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Q: Find the indefinite integral. (Use C for the constant of integration.) -0.2x е dx

A: We have to find indefinite integration: ∫e-0.2xdx In this case we use substitution method, so let…

Q: The rate of change of temperature, in degrees Fahrenheit per hour, is given as a function of the…

A: We are given the following figure. We need to find the following.

Q: valuate the indefinite integral. (Use C for the constant of integration.) dx

A:

Q: ne value of fe*d by dividing the range of integration qual parts using Simpson's rule is aces)…

A: Introduction: The formula of Simpson 13rd rule for n equal intervals is given by,…

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: The integral dx If the integral converges, enter the value of the integral in the blank below. If it…

A:

Q: 1. Let f (x) = ln(-x). a. What is its domain? b. Find and simplify its derivative. How does this…

A: Use differentiation

Q: A tank contains a brine solution. Fresh water enters the tank at a rate of 5 gal/min while the…

A:

Q: "ind the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: To evaluate the indefinite integral: ∫x2x-8dx Solution: Degree of numerator is greater than…

Q: Find the indefinite integral. (Remember the constant of integration.) dx xº - 8

A: Given query is to find the value of the integral.

Q: Q1- Express of the integral in term of Gamma function and simplify * x*e-2x dx. where possible

A: Use gamma function

Q: A curve for which y" = x passes through the point (1, –1) with .3 a slope of . Find the value of…

A: Given- A curve for which  y"=x passes through the point 1,-1 with a slope of 32. To find- The value…

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

A: Integration

Q: An office contains 1000 ft 3 of air initially free of carbon monoxide. Starting at time = 0,…

A: An office contains 1000 cubic ft of air initially free of carbon monoxide. Percentage of smoke…

Q: problem in the photo attached

A: definite integration.

Q: 1- What are applications of integration? 2- What are logarithmic functions? Calculate the area under…

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Q: A cylinder is changing size in a such a way that the volume remains constant 187 cubic meters.…

A: 3)d) Given Volume of cylinder = 18π Let r be the radius and l be the height dldt=-2 m/hl=2 m

Q: valuate the indefinite integral. (Use C for the constant of integration.) 6 - x2 dx

A: We need to substitute for this integration

Q: Find the indefinite integral. (Use C for the constant of integration.) ーx)3(2 - x) dx

A:

Q: QD: Use total differential to find the percentage error in calculating the area that cut from a…

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Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 1 m, at what…

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Q: The area of the region in the first quadrant bounded below by the curve y=e* and above by the curve…

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Q: „log3(cosh x) + csch x ) tanh x dx

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) - 2x)º dx

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Q: integral from -5 to 4 of absolute value x^2-4 dx

A: Given, I=∫-54x2-4dx

Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

A:

Q: The rate at which a substance grows is given by R'(x) = 195 e 0.5X, where x is the time (in days).…

A: This question can be solved by integrating R'(x) with proper limits.

Q: The tube cross-section shown has inner radius of 3 cm and outer radius 6 cm and within the tube…

A: This question is about application of derivative

Q: integral from 0 to 1 of square root of (1- square root of x) dx

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Q: 8. dx. Find the indefinite integral

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Q: Find the indefinite integral:  ∫ x (x - 8)1.5 dx. Hint: Use Integration by Parts.

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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: 1. A pebble is dropped in a calm pond causing ripples in the form of concentric circles. The radius…

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Q: Gas is escaping from a spherical balloon at the rate of 2 cm /min. Find the rate at which the…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) (e dx

A: Here we integrate the given function.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. - eu du (6 - e4)²

A: topic- indefinite integral

Q: wing integrals: 7.S In x x√4 lnx-1 dx 18.f ex 3-4e2x dx

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Q: „log3(cosh r) + csch x) tanh x dx

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Q: 5 cosh 2t +-sinh 2t 2 -2t 3. L{

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Q: 1- What are applications of integration? 2- What are logarithmic functions? Calculate the area under…

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Q: integral of x ln(x+1)

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) -6r dr

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Q: The rate at which a substance grows is given by R'(x) = 180 e 0.3X, where x is the time (in days).…

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Q: The rate of growth of a population (in millions per year) in the year x is approximated by f(x) = xe…

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Q: A spherical snowball is melting at a rate of 9.2- min snowball's volume is 4500 cm³? The radius is…

A: Note that, the volume of the sphere is given by: V=43πr3 So,  dVdt=43π(3r2)drdt⇒dVdt=4πr2drdt...(1)

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.