The diagram shows part of the curve y = 2ln(3x + 2), meeting the x-axis at the point P and the y-axis at the point Q. The normal to the curve at Q cuts the x-axis at the point R. y y – 2ln(3x + 2) P' 0 Find the area of the region bounded by the x-axis, the curve PQ and the line QR.

Q: Q-1- Find the area of the region bouncledby the Curve y= xe and the XaaXis froam X=o to x = 4 ?

A: To find the area of the region bounded by the curves

Q: Q45.a) Find the area of the region enclosed between the curves y= cos(2x), y=0, x=r/4, x- 1/2…

A: Make the graph and than use the integration to find the area.

Q: 11. Find the area bounded by the curve 5y²-16x and the curve y²=8x-24. A. 30 sq.units C. 16 sq.units…

A: We need to find area bounded by curve.

Q: 2. Sketch the curve y=3x2+1 between x=-2 and x=4. Determine by integration the area enclosed by the…

A:

Q: Q. 1. a) Find the area of the region enclosed by the curve y = x² -2 and by the line y = 2. y=x²-2…

A:

Q: Find the area between the curve y = cos (2x) and the line joining the points (pi/4, 0) and (pi/6,…

A: Area of the region is (2-√3)/4

Q: - (b) Let R be the region bounded by the curves y Midpoint Rule with n= 4 to estimate the area of R.…

A:

Q: x² and (d) Find the area A of the region R under the line y x +2, above the parabola y between the…

A: Given that, Equation of parabola, y=x2  ..... (1) Equation of line, y=12x+2   ... (2)   We have to…

Q: ind the volume of the resulting solid if the region under the curve  y = 8/(x2 + 3x + 2)  from x =…

A: Consider the curves y = 8x2+3x+2, x=0, x=1 about x-axis For this region of the disk is y = 8x2+3x+2…

Q: 5 for 0<x < 7. %3D Calculate the area of the segment between the curves y = sin x and y =

A: To find the area between the curve

Q: Find the area of the shaded region 14 12 bounded above by y = 2, bounded below by y = cos(x) + 1,…

A:

Q: 1+x² 1. Find the area of the region bounded by the curve y=- and the lines y = 0, y = x, x = 2. 2x2

A:

Q: Show that the area of the region in the first quadrant en-closed by the curve y = (1/a) cosh ax, the…

A: First of all, consider the graph for curve y, the coordinate axes and the vertical line x = b.The…

Q: Find the area of the region enclosed between the curves y= sin(2x), y=0, x= 0, and x= 3n/4 (Sketch…

A: Sketch the graph and integrate function in given interval.

Q: Q.8 Find the area of the curve bounded by the curves y = x* and y = 3x+4.

A:

Q: Q.2 A. (i) Find the area of the region bounded by the curves y = x² - 4x + 4 and y = -x² + 20 .

A:

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

A:

Q: f the region enclosed by the Curve y= Sin (Tx/2) and the tind the area line

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 6 - 6…

A: The given region is r=6-6sinθ, r=6.

Q: d the area of the region bounded by the curves: y = cos(nx) and y = -1 + 4x²

A:

Q: 2. Find the total area of the region between the curves y = sinx and y = cosx for 0<xs 37 2

A:

Q: 1. Sketch the region enclosed by the given curves: y = e*, y = x² – 1, x = -1, x = 1. Find the area…

A:

Q: Find the total area of the region between the curves y = sin x and y = cos x for 0 &lt;=x&lt;=…

A:

Q: %3D Q.5 Find the area between the curve x=4ay, the x-axis, and the line x 2.

A:

Q: 44.a) Find the area of the region enclosed between the curves y=1+x, y=1+4x, and y=3-x (Sketch the…

A:

Q: 1) Find the area of the region bounded by the curves: x=2y2 and x=16+y2 2) Find the area of the…

A: Important points: 1. First we will draw both the parabolas by finding their vertex. 2. Then we will…

Q: (b) Find the area of the region that lies inside the first curve and outside the second curve. r = 1…

A:

Q: Find the area enclosed by the given curves y = tan(7x) and y = 2 sin(7x), where -T/21 < x <T/21. You…

A:

Q: Find the area of the region between the curve y = sin t andthe t-axis from t = 0 to t = 2π.

A: the area of the region between the curve y = sin t andthe t-axis from t = 0 to t = 2π is defined as…

Q: Sketch the region bounded above by the curve 7e sin(Tx), the x-axis, and r = 1, and find the area of…

A: The graph of the above function is :

Q: Find the area of the region bounded by the given curves. y = sin n y = x² – 6x

A: The given curves are y=sinπx6, y=x2-6x. Find the area of the bounded region.

Q: 9. Find the area of the region between y = sin 0 and y = sin e , between 0 = 0 ande = n/2. %3D

A: To find the area of the region between,  y = sin3 θ  and y = sin θ Between θ = 0 and θ = π/2 The…

Q: problem in photo attached

A: Consider the given functions:

Q: 8) Find the area of the region between the curve x = e- e15t Le-14t and the x-axis, 0 <ts In 9. y=.…

A:

Q: 42) Find the surface area of the solid that results when the region in the first quadrant bounded by…

A:

Q: 1. Find the area between y=x and y=x' fromx=-1 to x-1. 2. Find the area of the "triangle" region…

A:

Q: 3. Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis…

A: Follow the procedure given below.

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

A: Given that the curves are    y = sin(x) , y = ex , x=0 and x = pi/2 Here we have to find the area of…

Q: Find the area enclosed by the given curves. Find the area of the region in the first quadrant…

A:

Q: Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and…

A: Given: Find the area of the “triangular” region in the first quadrant bounded on the left by the…

Q: Find the area between the curves 피/5 y = e y = 10 tan -x) + 1, 0< x < 4 16 Area

A: According to question,Given curves,y = e-x5y = 10 tanπ16x+1,0≤x≤4

Q: Q9// From x = -3 to x = 1, sketch and find the area of the region bounded by the curve x = F/y+ 4…

A: Given: To Find:

Q: enclesed by ) Find the gavea d the region the line ) x-In3 and the curves y= ex and y-ex

A: We will solve the problem.

Q: (4) Find the area of the region bounded by the curves y = sinx, y = cos I, I = T x = 3π/2. You will…

A:

Q: (a) Find the total area of the region between the curves y = sin x and y = cos x for 0 < x < 3x/2.…

A:

Q: Find the area of the region that lies above the x-axis, below the curve x=t2+5t+8, y=e-t with 0≤t≤1.

A: Given that, x=t2+5t+8 y=e-t Where 0≤t≤1

Q: Sketch the region bounded above by the curve 8e Round your answer to four decimal places. *sin(T2),…

A:

Q: Find the area of the region bounded by the two curves: y = sin 2r, y = tan r, for z 20, and r< 2.

A: Here, y=sin(2x) , y=tanx , 0≤x&lt;π2 Region bounded by these two curves in the interval 0≤x&lt;π2 is…

Q: ー元 Q.3 Sketch the region enclosed by the curves y = sec' x, y=x² +1, xr=- 4 and find 4. its area.

A: Sketch the region and integrate the function with x from -π/4 to π/4.

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.