f(x)=6cos2x Find the area of the region enclosed by the tangent line of the function f(x) at x = 2 and the coordinate axis

Q: 1) Determine the area of the region bounded by the graph of the function and the tangent line to the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the area between the curve y = x² + 8x + 12 and the x-axis from x = -2 to x = 0. (Give an exact…

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Q: Find the area of the region between the curves y = sin(x), y = sin(2x), x = 0, and x = t/2. Area…

A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: Find the area A of the region that is bounded between the curve f(x) = -2 sin () and the curve g(x)…

A: Given that we have to find the area of the region that is bounded between the curve f(x)=-2sinx4,…

Q: find the relation error use the trapezoid rule to approximate the definite integral. Use n=4 xe* dx

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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 enclosed by the curves f(x) = 33 - x² and g(x)=x². The area (rounded to two decimal…

A: The region bounded by the curves fx=33-x2 and gx=x2 The formula to calculate the area bounded by the…

Q: . Find the area of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: Find the survace area of revolution about the x-axis of y= 4sin(2x) over the interval x is greater…

A: Given: The curve y=4sin2x for 0≤x≤π2 To find: Surface area of revolution of given curve about…

Q: Find the area of the region enclosed by the tangent line of the function f(x) at x = 2 and the…

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Q: The area between y= 2sinx and y = sin2x for 0<x ST is

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Q: Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

A: The given two curves are,

Q: Use the right-endpoint approximation to approximate the area under the curve of f (x) + 1 on the…

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Q: Can you help with this problem step by step?

A: We know that area of the region bounded by curve y=f(x) and x-axis from x=a to x=b is

Q: by the x-axis (y = 0)

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Q: sin(z)

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Q: Find the area of the region bounded by the graph of f(x)=sin x and the​ x-axis on the interval…

A: Formula used:∫sinxdx=-cosx+C   , C is the constant of integration

Q: . To solve this problem, you should use the function on the same line as your ω value. ω = 0 ⇒ f(x)…

A: Given,

Q: 24) Using Numerical Integration to estimate area between curve (y=2-x²) and line (y=-x), with n=3

A: We have y=2-x2, y=-x then intersection point is -x=2-x2 ⇒x2-x-2=0 ⇒ x2-2x+x-2=0 ⇒ (x-2)(x+1)=0⇒x=-1,…

Q: In the diagram below, the region between the graphs of y=2 sin¬x and y=rx, in the first quadrant, is…

A: Finding the area of the shaded region

Q: Can i get help step by step with this problem?

A: Given,

Q: Area under the curve y2 = 4x from x=1 to x=4

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Q: Calculate the area confined by between the portion of the graph of the function f(x) = -(x – 2)² + 4…

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Q: find the relation error use the trapezoid rule to approximate the definite integral. Use n-4 xsinx…

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Q: Use a definite integral to find the area of the region between the curve y = 17x and the xX-axis on…

A: Area is the double integral with respect to y and x. It is known that at x-axis that is y=0. We have…

Q: f (x) = x² and g(x) = 3x – x2 Зх — 3. Find the area between the two curves by integration.

A: We have to find area

Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

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Q: find the relation error use the Simpson's rule to approximate the definite integral. Use n=4, , Inx…

A: Simpson' s rule for integration:…

Q: 1. Find the area of the region bounded by the curves y=sin X16 , y = 0, and x = 6 obtained by…

A: topic - Area bounded by curves

Q: Find the area bounded by the curves y=sin x and y= cos x from x =0 tox= 7. Make a sketch and shade…

A: The region bounded by the curves y=sinx and y=cosx from x=0 to x=π

Q: Using the trapezoidal rule with n = 4, estimate the integral / (x (x+1)² dx.

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

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Q: Find the area of the region that is bounded above by the curve f(x) = (x + 2)² and the line g(x) = 4…

A: NOTE: Refresh your page if you can't see any equations. . here we have first, we need to find the…

Q: Find the area of a region between the z-axis and the graph of f(r) = r² – x² – 2r. Define the term…

A: Given function is f(x)=x3-x2-2x

Q: 4. Find the area of the region bounded by y = sin x) and y = x² – 8x. Be sure to provide a graph of…

A: The region is bounded by,      y=sinπ8x and y=x2-8x

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

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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: Find the area of a triangle bounded by the y axis, the line 2 f(x) = 6 - x, and the line…

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Q: Use a definite integral to find the area of the region between the curve y = 3x and the x-axis on…

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Q: Find the area bounded by y2 = 4a(y - x), y2 = 2a(x + 2y – 3a) and the x-axis. Show complete solution…

A: To find the 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: Find the area of the segment cut off from the curve y = sinx, 0≤x≤nt by the line y = 1/√2. HT 1/2 y…

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Q: Find the area between the curve  y = x2 + 10x + 16  and the x-axis from  x = −2 to x = 1.  (Give…

A: To find the area between the curve y=x2+10x+16 and the x-axis from x=-2 to x=1. This is given by…

Q: 3. Find the area between the curve y = 2sinx cos x and the x-axis within the interval [0,2π].

A:

Q: 1. Find the area bounded by the curves between the curve y=1+x and the line y-1 x

A: area between curve

Q: The area between the curves f(x)=x and g(x)= x^2 on interval [0,2] O 2

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Q: Find the area (sq. units) covered by the line y = -Gx+ 3) from x1 = -8 to x2 = 0.

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Q: Integrate using trigonometric substitution Integral of x/(x^2-1)dx

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Q: Approximate the area under the curve f(x)=sin2(πx) using the midpoint approximation rule with 3…

A: Using a sum of midpoint rectangles calculated with the given formula

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.