H.W: Use the Trapezoidal Rule with n=6 to approximate. Here f(x}=sin2x,a=0,b=x.

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

A:

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule n=10 with to approximate…

A:

Q: find the domine of the function y(t)=sin 4t

A: Consider the given function: The domain of a function is the set of input or argument values for…

Q: Q. No.1: Evaluate the following using Trapezoidal rule 2 t (a) |t sin t dt (b) ; dt 5+ 2t

A: The given integral is ∫0πtsint dt Let ft=t sin t   let n=6 Therefore, a=0, b=π,  calculate h using…

Q: dy Given y = In(tan 0), find 0 such that 4, where 0< 0 <T 2

A:

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

A:

Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: Find the length of the curve. x = cos t y = sin t

A:

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: Given that Sinh Ys 2. fnd sech x, eanh y with draw atiangle

A:

Q: Given the implicitly defined function sin(a*y) + y = + y dy dy and find at the point (r, y) = (0,…

A: Use the chain rule of derivative and substitute the given value then simplify to get the send and…

Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

A:

Q: Find the length of the curve y = ln(sec x ), x is an element of [0, pi/4]

A:

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: Given the equation x In(y) dz = z Arctan(3y). Assuming z as a function of variables x and y, find ar

A: To partially differentiate the function z with respect to x.

Q: d?x +x = secy %3D dy2

A:

Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: The Tschirnhausen cubic is the curve given by the equation x^2=y^3+3y^2 At which point(s)…

A:

Q: Find the speed of the cycloid c(t) = (4t −4 sin t, 4−4 cos t) at points where the tangent line is…

A:

Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

A:

Q: cos(x) dx

A:

Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

A:

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

A:

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

A:

Q: Find the length of one arch of the cycloid 1 8(t- sin(t)), y = 8(1 – cos(t)).

A:

Q: Given the equation r In(y) = z Arctan(3*y). Assuming z as a function of variable dz and y, find

A: The given equation is xln(y)=ztan-13zy ........................................ (1)  Here z =…

Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

A:

Q: Consider the following. x = 2 sin(t), y = 3 cos(t), 0 <t < 2n dy d?y Find and dx dx2 dy dx d?y dx2…

A:

Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/3 In (2 + v 2 ) – - In (1)

A: Since you have posted 2 questions we will solve one for you please resubmit the question. Given:…

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0≤ t ≤ π

A:

Q: Solue d?3e 2 +4x=5in zt using methoel I Vorintion of parameters .

A:

Q: (a) y = arctan (b) y = v1-x' arsin(x)

A:

Q: S(r* +x )dx Approximate with n = 4 using Simpson's Rule Trapezoid Rule.

A:

Q: Find dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 &lt; t &lt; π   For which values of t is…

A:

Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

A:

Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

Q: Find the length of the curve. r(t) = cos(5t) i+ sin(5t)j + 5ln(cos(t)) k, 0<t< n/4

A: r(t)=cos(5t)i+sin(5t)j+5ln(cos(t))kWhere, 0≤t≤π/4

Q: Use the variation of parameter method to find a particular solution d²y * + 4y = sec? (2t) Yp of…

A: Consider the provided differential equation,

Q: Given the implicitly defined function sin(r²y³) + y³ = r + y I dy dy and dx2 find at the point (x,…

A: Topic = Derivative

Q: he length of the curve y = sin(3X) from x = 0 to I= is given by

A:

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule n=10 with to approximate…

A: aGiven∫241lnxdx,n=10Using Trapezoidal…

Q: Find the length of the curve. x- 5 sin t+ 5t, y= 5 cos t, 0 st< O A. 5T O B. 20 O C. 10 O D. 30

A:

Q: The integral that represents the length of the curve 7(t) = (t, cos (2t312), sin (2t312)), where Ost…

A:

Q: 5. Given the equation xy = Arctan(ye*) where z is a function of a and y, Əz əz find and ar ду

A:

Q: Given the eguation y In (x +y + 1) = 8, evaluate dy Assume that the equation implicitly defines y as…

A: Differentiate with respect to x

Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

A:

Q: Find the length of one arch of the cycloid x= 6(t-sin(t)) y= 6(1-cos(t))

A:

Q: For the smooth curve, find any points where the tangent line is either horizontal or vertical. x(t)…

A:

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.