Using Simpson's rule, the approximation value for the o sin(x)dæ is : Select one: a. 1.024 b. 0.425 c. 1.425 d. 0.325

Q: Find the arc length L of the graph of the given equation from P to Q or on the specified interval. y…

A: Solution is written in below steps.

Q: A. Find the area enclosed by each of the following curves. T= 4 sin e

A:

Q: The slope of the tangent line to the graph of f(z) COS at a is Select one: O a. 00 2 Ob. 2

A: we hav eto find the slope of the tangent line of the given graph at a=π/2

Q: Question ): The integral that represents the length of the curve y = tan(2a), where <a <, is the…

A: Given y=tan2x

Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

A:

Q: Show that coshr + sinh r = e" and cosh r - sinhr = e. Hence, deduce M MOUTMOUT cosh? a – sinh? r 1.…

A:

Q: find the total length of the arc of the function 6xy = x^4 + 3, x=1 to 2.

A:

Q: Find the exact length of the cur x =t sin t y =t cos t for 0 <t < 1.

A:

Q: The approximation of I = S, cos x? dx using composite Simpson's rule with n 3 is: -1.5412 O This…

A: Formula :     The formula for composite simpson's rule is     ∫abf(x) dx ≈∆x3 [fx0 +4 fx1+2fx2+4…

Q: Find the length of the following curve at the given distance. Rie). cos'e ?a sin? t } Cos t i 2

A: Given curve is R→t=cos3ti^+sin3tj^ where 0≤t≤π2. We have to find the length of the given curve at…

Q: Find the arc length of the given curve on the specified interval. This problem may make use of the…

A: Explanation of the answer is as follows

Q: find f'(l.os) with h=o .05 If fuXsinx using three puints formula

A:

Q: Find the measure of the given arc. тJML M K N 60°

A: Solution

Q: Compute the exact area that is inside the circle (r = 14) and outside the petal of the flowered…

A:

Q: of Use the definiion Çaplace to determine the fessz e

A:

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

A:

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

A:

Q: 29. Area = %3D EF, FH, and HI are tangents. EI is a diameter. E 2ft.F J 8ft. H

A:

Q: 2t k, then the distance traveled over 0Sts In 3 is:

A:

Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: Which of the following is(are) true? (Choose all applicable answers.) O cosh z = e +e* 2. O coth a e…

A:

Q: The approximation of I = , tanx dx using composite Simpson's rule with n-5 is: None of the choices O…

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: Let / = x tan(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

A:

Q: 4. Use the arc length formula to show that the length of a linear function f(x) = mx +c on the…

A:

Q: If Wallis is used to integrate sin rcos zda, what must be the value of a? A. 00 B.1 C.O D.

A: In wallis integration, to find the value of alpha

Q: What is the arc length of DF in tems of n? 120 3 cm E OA. б ст O B. TT cm O C. 2п ст D. Зп ст

A: We know, length l of an arc of a circle having radius r units and subtending an angle θ (in radians)…

Q: S arctan y dy y3

A: Let's evaluate given integral.

Q: Find the arc length of the graph of the function f(x) = ln(cos(x)) ㅠ π [153, 5 Use the tables to…

A: Arc length of y=f(x) on a, b is  L=∫ab1+f'x2dx We have f(x)=lncosx given interval π9,π5

Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: While evaluating the approximate value of 20 x² dx, using Trapezoidal rule, taking 3 h = 0.5, the…

A:

Q: Find the arc length of the graph of the function over the indicated interval.

A:

Q: What formula would be used to calculate the right rectangle approximation of " (sin x · cos x)dx…

A:

Q: 4. Find the length of the arc for: r = e° for 0 se ST.

A:

Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: Find dx or y' of the following functions and make any a. y = cot(Ve" ) tanh(e") b. Y =…

A: taking ln both side

Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: 3) by using a

A: sin(12π13)=f(a)+f'(a)*h=cWe need to break it in Taylors series:f(x±h)=f(x)±hf'(x)±h22f''(x)±...

Q: If y= sin?r+ tant, x= - In(- cost) – e inr, find the value of y' when 1= ". 2 2+ Vze VE 2-Vze 2

A: Given,y = sin2t + tantx = -ln(-cost) - esint

Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: The approximation of I = S, tanx dx using composite Simpson's rule with n=5 is: O 0.6158 O 0.6236…

A: First option is correct

Q: Given: z = cos(xy) dz Find: ду dz ду dz - tan(xy) = -x sin(xy) ду dz = tan(xy) = -y sin(xy) ||

A: Given: z=cos (xy)Find: ∂z∂y=?

Q: If sint = - - and t is in the 3rd quadrant, then tan t %3D V45 45 O V45 V45 2 V53 O O O

A:

Q: Find the arc length of the graph of the function f(x) : In(sin(x)) over the interval 11 7

A: Let's find.

Q: dr Let A be the area of a circle with radius r. If dt dA when r = dt 3, find 7. Present the exact…

A: Given ; A be the area of a circle with a radius r. drdt = 3 r=7

Q: The approximation of I = tanx dx using composite Simpson's rule with n-5 is: O 0.6158 0.6165 None of…

A:

Q: If y = tan u, u = v - and v = In x, what is the value of at x = e? dx sec?e 1 O Option 4 O Option 3…

A:

Q: T= 8 cos 30. with /met: A =

A:

Q: Find the area inside the circle r = –3a sin 0 and outside the cardioid r = a(1 – sin 0), a > 0. -

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.