rsin x If f(x) = m* V1 + t²dt and g(y) = f(x)dx, find g" SHOW WORK!!! %3D Find the number a such that the line x = a bisects the area under the curve y = on the interval [1,4]. SHOW WORK!!!

Q: Reversing the Order  of Integration Verify that

A:

Q: he force F newtons acting on a body at distance x metres from a fixed point is given by F = 2x2 +…

A:

Q: for the Area below ..By using vertical rectangular strip ... what are the limits * ?of integration…

A: To find the limit of integration.

Q: Q.2 Find area under the curve y = x² +1 over the interval [0,3], Using Riemann sum.

A:

Q: I found a textbook example which intergrates an area function to find the volume of a solid of…

A: For this question radius= (x-1)^2 from x=0 to x=2

Q: An aircraft oncoming the airport is 0.5km from the antenna that has a maximum dimension of 3 m…

A: Given: Let us consider a plane approaching the airport is 0.5 kilometres away from the antenna,…

Q: The shaded region R in the figure is bounded by the line = 4r and the parabola 1- r2. Use the washer…

A: Given :         y=4x , y=x2Find Rx , Area , Volume .

Q: Ris the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=1 and x=3.…

A:

Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

A:

Q: -1 -1 Differentiate xe 1 2 and hence integrate 2 dx.

A: Let g(x) =x e-12 x2 then x -derivative of g is given by dgdx=ddxx e-12 x2  now , using product rule…

Q: The integrand of the definite integral is a difference of two functions. dx 15 15 Sketch the graph…

A:

Q: Let R be a region bounded by x-axis, the curve y= cos.x between x= - 2 and x=-lines. If the region…

A:

Q: x2 = 2 - y and y =x – 1 are bounded. Identify its area. Vertical strip A = (Vu - yı) dx Horizontal…

A:

Q: V1+(y')* - dx integral. Find the y(x) function that minimizes the

A: To find -

Q: Using a midpoint approximation with five rectangles, approximate the area under the curve f(x) = 2 –…

A: According to mid point approximation for a function f(x) which is continuous over the interval [a,b]…

Q: The boundaries of the shaded region in the figure are the 4 y-axis, the line y = 1, and the curve y…

A:

Q: 6e at x-b First find where the two curves meet. y = 5e" meets y = 6e where b Then Area = - f(x) dx…

A:

Q: Set-up the definite integral that would compute for the Moment of Mass about the x-axis of the…

A: This is to find the Moments of mass Mx and My.

Q: Find the area of the region bounded by the curves y = 1/x , y = x and y = 4x in the first quadrant.…

A:

Q: 2. We want to integrate a function over the region bounded by x = y2 - 1 and x = /1- y2. What should…

A:

Q: Sketch the graph of the curve y = (x – p)(x – p – 1)(x – p – 2) Shade the area of the region bounded…

A:

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

A: First we use Right endpoints (Right Riemann sum) to find the area of the curve then we use left…

Q: 6. Using the trapezoidal rule with three ordinates an estimate of the area under the curve y = sinx…

A: As per our guidelines, we are allowed to answer only one question. Since, you have asked multiple…

Q: pproximate the area under the curve f(x)=x^2+ 1 from x = 2 to x = 5 using a Left Endpoint…

A: left end point sum

Q: Solve parts these 2 parts of the question. Image attached.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (a) Suppose f"(x) = 0, what can you say about f (x)? Write it in general form. (b) Find the area of…

A: .

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A:

Q: Find the area bounded by the curve given by f(x) = - x ^ 2 - x + 2 and the z-axis on the interval [-…

A: Given data  Curve f(x)=(-x^2-x+2) on interval [-2,1]

Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

A: Given: To find the area of the region bounded by the graphs of the equations

Q: Consider the area bounded by f(x) = e-3x+2 and the x-axis over the interval [0, 4]. In your written…

A: Given function is fx=e-3x+2 interval is 0,4 Midpoint Rule:-  Use the midpoint rule of two sub…

Q: QI] Find the area bounded by the following curves: A] y 5-x2 and y 2+ 4. BJ y = -Vx, y -x+3 and y 0

A:

Q: 4. The area of the region between the curve y=x and the line y-4 is divided into equal partitions by…

A: Solution

Q: Q3) Find the average value of the function f(x)=√cos 4x+1, on [0,1 Q4) Using Numerical Integration…

A:

Q: An area is bounded by the curve x ^ 2 + 10y - 1600 = 0 and the x-axis . Find the moment of inertia…

A: 1st we need to identify the region R bounded by given curve and x-axis .  Then for moment of inertia…

Q: x from x = 0 to x = 2 using a Right Approximate the area under the curve y = Endpoint approximation…

A:

Q: The curve with function y = 6 + x³ is defined. a) Find the area under the curve (Hatched area) b)…

A: a.        Area(A)=∫03ydx          =∫036+x3dx           =6x+14x403            =18+814…

Q: The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = VT. Find the…

A:

Q: The boundaries of the shaded region are the y-axis, the line y 1, and the curve y Vx. Find the area…

A:

Q: Using Integrating Factors Found by Inspection. 2 2 1)dx + x(x´y' + 1)dy = 0 2 2 2. y(x'y -

A: The solution is given as

Q: The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = VT. Find the…

A:

Q: f valuate area bounded by the parabola X 2y-y the * *y ond integral using double

A:

Q: Find the area of the region that is enclosed between the curves x² = y and x = y – 2 integrating…

A: Given that: x2=y    .........(1)x=y-2 .........(2)

Q: Let R be a region bounded by x- axis, the curve y= cosx between x= -lines. If the region Ris…

A:

Q: etermine the area bounded by the curves f(z) = 1² – 18x + 36 and g() = -9x + 18.

A: This question is based on application of Integration.

Q: Find the absolute extrema for the function f(x, y) = y – x²y over the region enclosed by y = 4 – a²…

A: Given:f(x,y)=y-x2y over the region enclosed by y=4-x2 and y=0

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

A:

Q: 3. A frozen snack named Curvetto is in the form of a right cylindrical cone with a diameter of 2…

A:

Q: Q.1. Use (i). Midpoint rule (ii). Trapezoid Rule and (ii) Simpson's Rule with n = 6 to find the area…

A:

Q: Find the area under the curve. 2. y = 2x-x2 from x=1 to x=0

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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.