Evaluate the line integral|Vo•dr for the following function p and oriented curve C (a) using a parametricdescription of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integralsx² +y° +z?5711Tsts6.P(x,y,z) =C: r(t) = (cos t, sin t,for(a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasinglimits of integration.dt (Type exact answers.)

Given: φ(x,y,z)=x2+y2+z22Therefore:∇φ=x, y, z

Evaluate the line integral Vo• dr for the following function p and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals x² +y? +z? 57 11T p(x,y,z) = C: r(t) = (cos t, sin t, for sts | (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. dt (Type exact answers.)

Evaluate the line integral Vo• dr for the following function p and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals x² +y? +z? 57 11T p(x,y,z) = C: r(t) = (cos t, sin t, for sts | (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. dt (Type exact answers.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

See similar textbooks

Similar questions

Let F = -yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation. (a) Sketch the given curve C. (b) (c) Identify parametric representations for C₁ and C₂. Show that Green's Theorem is satisfied by evaluating both the line integral and the double integral for the given vector field F and curve C.
6a) Let A be the parabolic arc defined by the equation y = 8x – x over the domain interval [0, 8]. Sketch A on a set of coordinate axes below; identify the coordinates of both intercepts and the vertex. Estimate the length of A using the lengths of the two line segments joining either intercept to the vertex. Write the definite integral that represents the exact length of A. Do not evaluate this integral - just set it up and simplify it. Then, use technology to obtain an estimate of this integral's value. (report it correct to the thousandths place) b)
b) Sketch the curve given in parametric form by 1(t) = ti+ sintj + costk, 0 < t < 27, and write down an integral to determine its length. Calcu- late the length of this curve. → arc length
Use the IVT to prove that the curves y = x2 and y = cos x intersect.
Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation. (a) (b) (c) Sketch the given curve C. Identify parametric representations for C₁ and C2. Show that Green's Theorem is satisfied by evaluating both the line integral and the double integral for the given vector field F and curve C.
2.Proof that any tangent plane for the surface F( F) point = 0 passses through a fixed
Sec2X Q1) A) Evaluate the following integral: S: V1-tan2x B) Find the slope of the line tangent to the curve y = sin x at the point where x 3
3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively oriented circle x2 + y² = 9. (b) In which coordinate system did you evaluate the line integral? Explain why.
Calculate the line integral (imagen) where C is any curve that joins the point (1,1) with the (3,3).
SLntegrate h (x. y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0), goes along the x-axis to (1, 0). and returns to (-1.0) by the upper part of the unit circle.
Q1 Use the parametric equations to calculate the line integral'c p ds over the path c which is given " In the graph, Take P = 4 (0 ,2p) c2 a circular segment C3 is line segment C1 is line segment (0,-2p)
Sec2x Q1) A) Evaluate the following integral: J-tan x dx B) Find the slope of the line tangent to the curve y = sin x at the point where x =