25. What is the area of one of the petals of the rose curve r = 2 cos (20)? /4 /4 L con (20) do 8/" cos*(20) do A. В. 8 /4 /4 4/cos (20) do D. 2 cas (20) de -/4 CO OP -/4

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: x arcsin(x²) dx;

A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

A:

Q: Find the area of the region that lies inside both curves

A:

Q: Approximate the sol of x = sinx upto 4 decimal places by using Newtons method.

A:

Q: Evaluate the integration 2.5 o cos(x) with h=0.5 by using 3/8 Simpson Rule. Write your answer in 4…

A: The Simpson's 3/8 rule states,∫ydx=3h8y0+2y3+y6+ . . . + yn-3+3y1+y2+y4+y5+ . . . +yn-2+yn-1+ynWe…

Q: What are the new limits of integration if apply the substitution u = 6x + n to the integral sin (6x…

A:

Q: Approximate L Ve sin.xcos 2xdx Using trapezoidal rule. Use h = 10 . (Do calculation in 4 decimal…

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (-x* + 14x³ – 36z² +…

A:

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

A:

Q: 10 lemniscate ² = 4 cos 20 outside r = √ √√2

A:

Q: Only one of these calculations is correct to evaluate the definite integral V sinx dx Using the…

A:

Q: Write down an integral expressing the length of the curve y = cos x, 2 2

A: Apply the below formula: L=∫ab1+dydx2dx

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 (-24 x² – 10x³ -…

A: Given integral is ∫-4-1 -x4 -10x3 -24x2 -4x+4 dx Take  fx = -x4 -10x3 -24x2 -4x+4

Q: 1. Find the area under one arch of the curve y = cos- :cosex.

A:

Q: 3 Find tue Inde finite intyrel 2C In (x") doc at

A:

Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

A:

Q: 2 By using Trapezoidal rule, the value of "h" in evaluating - 2x + 6)dx , by taking 10 subintervals…

A: Solved below

Q: x = -sin 2y x = cos y --

A:

Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

A:

Q: State TWO (2) dissimilarities between Green’s and Stokes’ theorems.

A:

Q: In estimating L cos (5x) dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

A:

Q: 3 Estimate the integral 1 dx by Simpson's rule using n= 8. Vx3 + 5

A: Given that a integration and ask estimate value use Simpson rule when n= 8. In Simpson rule we can…

Q: Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of…

A:

Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

A:

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

A:

Q: What is the length of the arc y = (2/3)(x2+1)3/2 over the interval [3,6]?

A: We need to compute the length of the arc of the given curve over the interval [3,6]

Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

A:

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: Find an eqeation of the to the cune at the onuen povnt tangent line t 48) y=In(x²_ 7), (2,5)

A:

Q: What is the amount of the rotating body formed by rotating the region bounded by the y = cos x…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: What is the area under the curve y = cosx over the interval [0 ,π/2]?

A: Integrating the equation of curve in the given interval gives the area

Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

A:

Q: Calculate the area between the curves ² = 16 sin 20 and ²: = 16 cos 20 .Show by drawing

A: Given: The curves r2=16cos2θ , r2=16sin2θ To find: Area bounded by two curves  r2=16cos2θ ,…

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

A:

Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: 14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint:…

A:

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: 1 dx. cosh x

A: Rewrite the integral and using substitution method, we calculate the given improper integral.

Q: Sind the Partial derivadiVes of th Jiven fuctions with Ves Pect x(2-CoS 2y)

A: We have to find the partial derivatives.

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

A:

Q: Compute integral x^2cos(x^3+3) dx

A: Given : ∫x2cosx3 + 3dx

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.