Let f(x) 4x³ and g(x) = sin (Tx) and R is the region bounded by the two %3D functions on the interval [0,½]. a) Determine the equation of the line tangent to the graph of g(x) at x = }.

Q: Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R…

A: In this question we have to describe the area of region by using vertical cross section

Q: The area of the region bounded by the curves y =x and y = 20 –x² is drx|-'א-0 'J - »4,4 - S** |20…

A: We will use double integration to find area

Q: sketch the described regions of integration. 0 ≤ x ≤ 3, 0 ≤ y ≤ 2x

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Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A: The function is given as fx=cos x The interval is given as 0, π2

Q: (a) Express the area under the curve y = x 5  from 0 to 2 asa limit.

A: Given

Q: Find the x-coordinate of the center of mass of the region in the first quadrant that is bounded…

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Q: Let f(x) = x sin(2 x). Find its average value for 0sxs/2.

A: Given the query is to find the average value of function over the interval [0,π/2].

Q: Find the region bounded by the curves y = x and y = x² using a dx integral.

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Q: Approximate the area under the curve y-f(x) between x=0 and x=10 using the Trapezoidal Rule with n=5…

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Q: Consider the region bounded by the graphs of y = sqrt(x tan-1 x) and y = 0 for 0 <=x<= 1. Find…

A: Given,

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: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

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Q: nich integral represents the length of the graph of y = In(1 – x²) over the interval [0, ]:

A: here option A is true because length is given by =1+(dydx)2dx so here…

Q: Estimate the area under the curve f(x) = 2x from 0 to 1 using R4. Leave your final answer as exact…

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Q: Find the area of region that is bounded by the given curves. Integrate with respect to x and then…

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Q: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

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Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: Integrate f (x, y) = x over the region bounded by y = x, y = 4x − x^2, and y = 0 in two ways: as a…

A: First draw the graph of line y=x and parabola y=4x-x2. Then find the area of the intersection…

Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: Sketch the region R bounded below by the curve y = x², on the left by the line x = 1 and above by…

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Q: dx ¤(x+2)²

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Q: Find the area of the surface formed by revolving the graph of f (x) = x³ on the interval [0,1]…

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Q: Find the centroid of the region bounded by the graphs of y = x + cos x and y = 0 for 0<=x<=…

A: Graph is given below:

Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: Sketch the region of integration. [ [² x√ 1 + y³ dy dx

A: The answer as follows:

Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: Find the of region bounded by the functions f(x) : (В) sin x and g(x) = cos x over the interval [0,…

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Q: Identify the definite integral that represents the area of the region bounded by the graphs of y= x…

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Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: The area of the region bounded by the curves y =x and y = 20–x² is попe 4.4 O 4= " |20–x²-x| dr -4.4…

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: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine its area…

A: Sketch the bounded region.

Q: sketch the described regions of integration. 1 ≤x ≤ e2, 0≤ y ≤ ln x

A: Given  1 ≤x ≤e2 , 0≤ y ≤ ln x

Q: 2 (F(x) + x³)dx = ? %3D -1

A: Given that the area under f(x) in [-1,2] is 10br2 So,

Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

A:

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 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: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

A:

Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

Q: 0otained by rotating the region bounded by the given curves about the specified line y=x, y= 27, x-…

A:

Q: Q1/ Find the area of the region bounded by the given curve (y = x² - 5) and the curve (x = -) by…

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Q: Find the solid of revolution that results when the region under the graph of f(x) = xvsin x for 0< x…

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Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

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Q: Find the area above the curve y=Inx in the lower half-plane between x=0 and x=1. YA y=In x 1

A: The correct option is option d. From the curve determine the upper curve , lower curve. and the…

Q: = Compute the area of the region bounded by y hyperbolic or inverse hyperbolic functions. 1 √x²+16…

A: We compute the area of the region bounded by y=1/√(x2+16) over the interval [ 0,3 ] hyperbolic or…

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

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Q: Q3. The region bounded by the curve y = x² and the line y = 3x, is revolved about the line x = -3.…

A: We will find this using formula. As per our guidelines we are supposed to answer only one question.…