√x-2 set up Consider carve ye ² Sin (2 VX-2). parameterize this curre by letting X...
for b.
y= sin(x^2-3x+1)
og t par Set up, but do not evaluate, the integral required to compute the arc length of the curve cotr. y= 217from 0<x< /2. mense metied to compute Set up, but do not evaluate, the integral required to compute the surface area of the solid obtained by rotating the curve y=sin(x2 3x + 1), 0<x< 1 about the z-axis.
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The graph below is of the curve defined parametrically by: x-sin t and y- sin 2t -0 5 0.5 -1 (a) SET UP THE INTEGRAL TO FIND THE AREA OF THE REGION ENCLOSED BY THE CURVE AND EVALUATE (b) SET UP THE INTEGRAL TO FIND THE LENGTH OF THE CURVE TRAVERSED EXACTLY ONCE. DO NOT EVALUATE. SIMPLIFY TO JUST BEFORE MAKING A SUBSTITUION. (c) SET UP THE INTEGRAL TO FIND THE TOTAL DISTANCE...
x = t^2 - 2t + 4, y = t^3 - 6t^2
8. a) Set up the integral you would need to evaluate to find the length of the curve given in #3 if Osts 10. b) Set up the integral you would need to evaluate to find the arclength of the curve r = 4sin(30), traced out once. 3
Consider a particule in the box trial wavefunction φ(x)=(2/L)^1/2(sin(πx/L)+αsin(2πx/L)). Set up the expression for the energy functional Ε and optimize it with respect to the coefficient α.
2) Consider polar curre r=4coso and r=1+2 caso r=1+2 cos r=4coso B A a) Find ALL intersection points of the two curves, where osos2a, and Express them in polar coordinates b) Find the area inside the shaded loop of the curve r=1+2 cose C) Find the length of r=4cose from A to B as a increases, where A is the intersection of the two curres in quadrant II, and B is the intersection of the curve r=4cose with the positive...
3. (6 points) Consider the curve y = 2 - 2.22 restricted to the first quadrant. (a) Set up a definite integral that gives the length of this curve. Do NOT evaluate the integral (b) Set up a definite integral that gives the surface area of the solid generated by rotating the curve about the x-axis. Do NOT evaluate the integral.
Consider the following. x = 3 sin y , 0 ≤ y ≤ π, x = 0; about y = 4 (a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis. V = π 0 dy (b) Use your calculator to evaluate the integral correct to four decimal places. V = Please explain each step
a) Set up an integral that gives the length of the curve y^ 2 + y = 2x from the point (1, 1) to (3, 2). Do NOT evaluate the integral. b) Let R be the region bounded by y = 1 and y = cos x between x = 0 and x = 2π. Set up an integral that gives the volume of the solid formed by rotating R about the line x = −π. See the figure below....
Set up (but do not evaluate) an integral to determine the arc length of the curve y = x2 from x = 0 to x = 2. 3 (12pt) TT TT Paragraph Arial %D9 ==== T TY TO ABC Evaluate the integral found in the previous question using Simpson's rule with n = 4. Round your answer to 4 decimal places
4.Consider the curve described by the parametric equations x= sin(t)=cos2(t) ,y= sec(t). Verify that all points on this curve satisfy the equation x^2+y^2=y^4