Question 4 The area between y = 2sinx and y = sin2x for 0SxSn is None OA. 4 OB. 1 Oc. D.

Q: Question 1 Find the area between the curves y = x and y = 3x + 2.

A: The graph is shown below:

Q: Question 2 Calculate the area enclosed by r = 3 sin(3 0) for 0 <0<. 9л а) 8 3n b) O 2 c) 2 d) O 4 9n…

A: To find the area of the curve

Q: Find the area under the curve y=sin2x from x=0 to x=3pi/4 A. 2 B. 1/2 C. pi D. 3/2…

A: The curve y=sin2x from x=0 to x=3π4

Q: Question 19 Find the approximate area under the curve of f (x) =cos 5) from x = 0 to x = Tt, using 4…

A: Given- f(x)=cosx2 To find area under the given curve from x=0 to x=π, using 4 trapezoids. Here ,…

Q: QUESTION 10 Use a definite integral to find an expression that represents the area of the region…

A: Answer

Q: Question 2 A closed cylinder has a cylinder a height of 16 cm, radium r cm and the sum of surfaces…

A: We will prove given as shown below and approximate the area if radius increase from 4 to 4.02

Q: Question 25. Consider the integral -12 (Inx)zdx. I = Use the Simpson's rule to estimate i by using 4…

A: Given that  The integral 1/(lnx)^2 2 to 6 By using the Simpsons rule to find the value of i

Q: Question 10 Find the area enclosed between y = 3x and y = x3 -6-

A:

Q: UESTION 1 Find the area under the χ2-curve with 5 degrees of freedom to the right of the following…

A:

Q: Eualinte the indefinide integral Sin €) VAt cos ) dt

A: Integration = ?

Q: Question 23 Find the area under the curve y = x +3x- and the x-axis between x = 1, and x = 3 OA 28…

A:

Q: Question 7 The area bounded by y=1-x² and x+y=1 is submerged vertically in the water with the water…

A: Solution

Q: In each of the following cases, find the area of the region that lies inside the cardioid = 1+ sine…

A:

Q: Question 5 Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis.

A:

Q: QUESTION 4 Calculate the area between y = 7 - x² and x-axis from x = -1 to x=2 as shown in Figure 1.…

A:

Q: Question 2 At what value of the parameter b (b > 1) the area under the curve y = x2 on the interval…

A:

Q: Question 4. Find the area enclosed between the graphs = x² +1 and y = x+ 3. %3D

A:

Q: 4. Find the area between y sin(r) and y cos (2r) on

A:

Q: Question 2 At what value of the parameter b (b 1) the area under the curve y= c on the interval (1,…

A: Since you have asked multiple question, we will solve the second question for you.  If you want any…

Q: QUESTION 1 Find the area under the x2-curve with 5 degrees of freedom to the right of a) 1.6 % b)…

A: Here, given that degrees of freedom is 5 with right tailed chi square distribution.

Q: Question 10 Find the area enclosed by the curves y = 2x √3- π ® ²-√√4-. (A) А Im 21/12-4/09/20 7x D…

A: The equation of curves are: C1: y = 11-9x2C2: y = 2 To evaluate: The area enclosed by the curves.

Q: Question 4: 20 Find the area under the curve y = 3x2 - 8e4x + x+1 from 0 to 3.

A:

Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: Solve for the area common with r = 2 + 5 cos(20) and r = 5 sin(0).

A: Double integral is used to integrate the function of two variable over two-dimensional region.…

Q: Question 4. Find the area bounded by the indicated curves. y =x- 9x, y = 0

A:

Q: Find the area of the shaded region shown in the graph. y= 15 sin x 15 y= 15 cos x

A: Integration gives the function whose derivative is given. Integration is nothing but adding slices…

Q: 0. Find the area enehred by the following curves: * =y-2 and X =y.

A:

Q: Question 3: Find the area between the curve y = 6 – x² and the line y = -3x + 2.

A:

Q: Question 1.7 of 25 The area of the region that enclosed by f(x) = 2x-x² and y = 0 B) / A) 413 c) 3/4…

A:

Q: 4. Solve for the area common with r = 2+5 cos(20) and r = 5 sin(0).

A: Solve for the area common with r=2+5cos2θ and r=5sinθ.

Q: Question 3: Find the area between the curve y = 4 – x² and the line y = -x + 2.

A:

Q: r = 3 cos 0 a. re1+ cose

A:

Q: a- Graph r=3 sin 20 b- Evaluate the area inside the curve

A: We have to evelaute the area inside the curve r=3sin2θ.

Q: TT 10. Find the area that is bounded by r = sin 0 and lies in 2 3

A:

Q: Find the area c

A: Here we used the integration for finding the area

Q: Find the area of the shaded region shown in the graph. y = 12 sin x y= 12 cos x .

A: Given, The two curves y=12sinx and y=12cosx intersect atx=π2 in x∈(0,π)

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: Find the area of the shaded region shown in the graph. Ay y = 27 sin x 27 y= 27 cos x

A: Solution :-

Q: Set up the equation to compute the area inside the graphs of r = sin 0 anc r = 1 - sin 0

A:

Q: Question 4 Evaluate (x – 4) dA where Ris the region in the first quadrant enclosed between y = x and…

A:

Q: Question 43 > - 0.4x Find the area between the curves y = e' and y = 2.2x +1 from x=0 to x=4 Area =

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: 2. (a) Find the area of a region that lies inside the circle r 2 sin 0 and outside the circle r = 1.

A: As you post multiple questions According to the guideline I only solve the first problem please post…

Q: QUESTION 4 The area enclosed between the x-axis and the curve y=x² between x=1 and x=2 is:

A:

Q: Question 16 > Approximate the area under the curve y = with 4 subdivisions. x³ from x = 2 to 4 using…

A:

Q: Find the exact area inside r = 6 sin 0 and outside r = 3.

A:

Q: Find the area of the shaded region in the following figure y = sin x 5п

A: Find the functions f (x) and g (x).

Q: Question 3: Use Simpson's rule to evaluate the following definite integral: dx using n= 8 as sin x+2…

A: to evaluate the given integral

Q: Question 27 Determine the area bounded by f(x)=x²-x and x-axis. A —-unit² А B unit² Ⓒunit² D unit²

A: A detailed solution is given below.

Q: Question 4 Compute for the area between z = ±1.43.

A:

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

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.