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

Q: Find the area of the region between y = x sinx and y = x for 0 ≤ x ≤ π/2.

A: We need to Find the area of the region between y = x sinx and y = x for 0 ≤ x ≤ π/2.

Q: Find the area of the region bounded by the parabola y = x 2  ,the tangent line to this parabola at…

A:

Q: Find the area of the region under the given curve from 1 to 2. 5 y = X° + 4x

A:

Q: Find the area of the region enclosed by the curves y = 5sin x and y = sin (5x), 0sxST.

A: We have to find the area of the region enclosed by the curves  y = 5sinx , y = sin(5x) ; 0 <= x…

Q: Find the exact area of the region that lies beneath the curve y = 2 sin(x), 0 < x < n.

A:

Q: Find the area of the region that lies under the curve, y = sin x on the interval 0< x <;

A:

Q: Find the area of the region that is bounded by two curves y = sin x and y = cos x from x = 0 to x =…

A: Here, to find the area bounded by the curves y=sin x  and y=cos x from x=0 to x=π2. The region is as…

Q: Find the area of the region enelosed by the curve r=a{t-sint),y=a(1-cost),0sts2n.

A: Given query is to find the area enclosed by the curve

Q: Find the area of the surface formed by revolving the graph of y = 2e−x on the interval [0, ∞) about…

A: Consider The infinite curve

Q: Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and the…

A:

Q: Find the area of the region bounded by the two curves x = sin2y and x = cos2y from y to y = n 8

A:

Q: Sketch the region between y = sin x and y = cos x over the interval and find its area: [0, π]

A: Consider the given function as y=sinx and y=cosx

Q: (b) Find the area of the region by integrating with respect to y.

A:

Q: Find the area of the region bounded by the given curves. (22) y = cos x + 1, y = x, x = 0, x = 1

A: First of all we need to draw graph of all functions and then find out the common region and finally…

Q: Q1) Sketch the region enclosed by the curves and finds its area y=sin2x y=0, x=, x 4

A: The objective is to find the area of the region enclosed by the curves y=sin2x, y=0, x=π4, x=π2 The…

Q: Find the area of the region bounded by the given curves. y = sin2(x), y = sin3(x), 0 < x < A

A: The area between two curves f(x) and g(x) on an interval [a,b] is given by Given,

Q: Find the area between the curves y = cos x and y=−sinxfrom 0 to π/2:

A:

Q: The area of the region bounded by the curve y = a° – 3x? – x + 3 and y = 0 is

A:

Q: Find the area between the curve y = sin 2x and y = x^2

A: the area is 4/5

Q: Find the area of the region bounded by the curves: y=cosx, y=sin2x, x=0, x=pi/2

A:

Q: Find the area of the region bounded by the curves: y= cos x, y=sin4x, x=0, x=pi/2

A:

Q: Find the area of the region bounded by the parabola y = x², the tangent line to this parabola at (1,…

A: Given data: The equation of the parabola is y=x2. The given point is (a, b)=(1, 1). The slope of the…

Q: Find the area of the region bounded by the graphs of the equations y = sin r, y = sin' a, x = 0 and…

A:

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

A: The region between these two curves is shaded below

Q: Sketch the region enclosed by the given curves andfind its area.   y - cos πx    , y=4x2- 1

A: The given curves are y=cosπx   and  y=4x2-1. Sketch the region enclosed by the above curves as shown…

Q: Find the area of the region under the curve y = 6x² + 4x + 5 from x = -1 to x = 2.

A: Solve the following

Q: Find the area of the region that lies between the curves y = sec x and y = tan x from x = 0 to x =…

A:

Q: Find the area of the region bounded by the parabola y=x2 , the tangent line to this parabola at…

A:

Q: Find the area of the region bounded by the curve r = 8 cos 2θ.

A: We need to find the area of the region bounded by the curve r = 8 cos 2θ. Let us first plot the…

Q: Sketch the region enclosed by the given curves and calculate its area. y=4-x to the power of 2, y=0

A: The given equation is

Q: Sketch the region enclosed by the curves and find its area. y = cos 10x, y = 0, x = 20' 10

A:

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: Find the area of the region that lies between the curves y = sec x and y = tan x from x = 0 to x =…

A: We need to find the area of the region that lies between the curves y = sec x andy = tan x from x =…

Q: Find the area of the region enclosed by the curves y = sin x and y= sin 2x for 0sxsn.

A:

Q: Find the area of the region R enclosed by the curves y = x2 – 2x and the х — ахis.

A: Given: y=x2-2x

Q: Find the area of the region bounded by the given curves. y= x2, y = 4x - x2

A: The given curves are,   y= x2,  y = 4x - x2

Q: Find the area of the region enclosed by the curves y = 7sin x and y=sin (7x), 0≤x≤t.

A: The region enclosed by the curve y=7 sinx and y=sin(7x), 0≤x≤π

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

A:

Q: Find the area of the region enclosed by the curves y = sinx, y = cos x, x = 0 and x = 2n.

A:

Q: problem in photo attached

A: Consider the given functions:

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

Q: Sketch the region enclosed by the curves 4x+y2=12 and y=x then find its area using the appropriate…

A:

Q: 3 cos(9x), y = 3 – 3 cos(9x), 0 s xs x/9

A:

Q: Find the area of the region bounded above and below by the graphs y = sin 2x and y = cos 2x, where x…

A:

Q: Find the area of the region bounded by the curves y = x andy = sin x from x = 0 to x = π.

A: We have to find the area of the region bounded by the curves y = x and y = sin x from x = 0 to x =…

Q: Find the area of the region enclosed by the curves: y = sin x, y = cos x, x =0, x = 27

A: First draw the figure of y=sin x and y=cos x for the interval 0,2π.The graph is shown below, cosine…

Q: Find the area between the x-axis and the curve y = √1 + cos 4x, 0 ≤ x ≤ π.

A: Given that, Curve y(x)=1+cos4x We have to find the area between the x-axis and the curve 'y(x)'. As…

Q: Find the area of the region bounded by the curvesr = 2 cos 30 and x = y – 1.

A: The curves given are as follows: r=2cos3θx=y2-1 We know that x=rcos3θ, y=rsin3θ.…

Q: Find the area of the region between the curves y=x and y=x^3 on the interval [-1, 1]

A:

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.