Which integral gives the arc length of the curve y = e2x on the interval 2 < x < 4? a)o (1+2e**)dx b) (1+ 4e%*)dx C) e)

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: Set up a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y…

A: The length of the curve y=f(x) between the limits x=a to x=b is given by; L=∫ab1+dydx2dx

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Assuming that the line integrals in the options are over the unit circle centered at the origin (x2…

A: .

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: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

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

A:

Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: Which integral computes arc length of f(x) = 5/2 on 0, 1 1 1+ x° dx 0. 1 I V1+x³ dx 0. 1 49 7 1+x'…

A: Given function: fx=x52 on interval [0,1] Differentiate the given function w.r.t "x"…

Q: In the integral for the moment Mxz with respect to the xz-plane of asolid, why does y appear in the…

A:

Q: Assuming that the line integrals in the options are over the unit circle centered at the origin…

A:

Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

A: Given that The length of rod is π2 and the density of the rod is δ(x)=2-cos(x)  with 0≤x≤π2 To find…

Q: 2 How many subintervals does the composite trapezoid rule need to obtain the approximation of the…

A: Given function is

Q: The integral tan x sec?x dx is an improper integral of type I that diverges none of them is an…

A:

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: 6. Set up integrals to compute the arc lengths of the curves y = r², y = 26, y = x¹⁰ defined for z…

A: Let's find arc length of given curves on interval [0,1].

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: The arc-length of the curve y= :/ Vcos(31) dt , for 0<x<- is given by which of the following…

A: For the given statement

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 5  dx

A: Split tan5x into simpler powers tan3x and tan2x and change tan2x to sec2x-1 and simplify.…

Q: (b) Find a definite integral that represents the arc length of the curve over the indicated interval…

A: (a). Sketch the graph.

Q: Consider the curve segments: 1 S1: y = x from x = to x = 2 and 2. %3D S2: y = Väfrom x = to x = 4.…

A:

Q: Set up an integral that represents the arc length of the curve y 2xi from the point (0, 0) to (2,…

A: our objective is to setup the arc length formula

Q: To find the arclength of y = 3x² + 3 from æ = 0 to x = 4, which is the correct integral? OL = | VI+…

A:

Q: Evaluate the integral [(4x + 15y)da + (6x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A:

Q: arctan x dx Jo 2 + e* 8.

A: Given that a integration and we use to comparison theorem to determine this integral is convergent…

Q: Calculate the arc length of the curve y = cos 0 from 0 = 0, 0 = 27. Use the to series expansion of…

A:

Q: Evaluate the integral. arctan(5t) dt

A: Here we evaluate the integral∫ arc tan 5t dt

Q: Set up an integral that (if solved) would give the arc-length of the following curve on the given…

A:

Q: Set up an integral that represents the arc length of the function g(x)=sinxg(x)=sin⁡x for the…

A: We need to set up an integral that represents the arc length of the function g(x)=sinx for the…

Q: The area bounded by the ourves y= *", and y=2x iş revolved about the y-axis, Find the moment of…

A:

Q: Find the length of x = In(sin y) from y = to y = . %3D

A: The arc length of a function is the length of a curve fy on an interval a, b given byL=∫ab1+f 'y2dy…

Q: 2. Use the error formula to estimate the error in approximating the integral T/2 2 sin x dx using…

A:

Q: The curve segment y = x² from x = 1to x = 2may also be expressed as the graph of x = √ y from y = 1…

A: Given any function y=f(x) we can write this function in the form of vector function…

Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: Evaluate the integral. ∫arctan 4t dt

A:

Q: Write the integral that gives the arc length of y = cos x for –3 < x < 8. The use a midpoint Riemann…

A: Given that,            y = cosx , -3⩽x⩽8 Then     dydx= -sinx Since we have the formula to find the…

Q: y = sin(x), y = 2x

A:

Q: Use the definition of improper integrals to define dx Use your definition in 1. to show that the…

A:

Q: Evaluate the integral / (4x + 18y)dx + (27x – y)dy along the parabolic arc y = 2? from (0,0) to (1,…

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: Which integral expresses the arc length of y= In(cos x) from x = n / 6 to x = T |4? | sec(x) dx |…

A:

Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A:

Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: Set up the integral for the arc lengthof the function,y=43x32for 2≤x≤6if you integrate with respect…

A:

Q: Set up the definite integrals to compute the arc length and the surface area formed by rotating the…

A: The function is f(x)=4-x2 and the interval is [-2, 2] Equation of line is x=3.   To find: The arc…

Q: The area of the surface generated by rotating the curve y = 1 = cos(3x), where 0 ≤ x ≤ , about the…

A: Let's find Area of surface,when rotated about x axis.

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: Give an example of finding an arc lenght by integral.

A: According to the given information, it is required to given an example of finding an arc length by…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.