Question

In: Advanced Math

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following...

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following line integral with respect to arc length.

∫C(8x−6y)ds

Solutions

Expert Solution


Related Solutions

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....
Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane
If a circle C with radius 1 rolls along the outside of the circle x2 +...
If a circle C with radius 1 rolls along the outside of the circle x2 + y2 = 36, a fixed point P on C traces out a curve called an epicycloid, with parametric equations x = 7 cos(t) − cos(7t), y = 7 sin(t) − sin(7t). Graph the epicycloid. Find the area it encloses.
Multivariable Calculus [A] Consider the region R in the first quadrant that is outside the circle...
Multivariable Calculus [A] Consider the region R in the first quadrant that is outside the circle r = 1 and inside the four-leaved rose r = 2 sin 2θ). (A.1) Draw a sketch of the circle and the four-leaved rose (include the entire graph) and shade the region R. Feel free to use your graphing calculator. (A.2) Write the following double integral as an iterated integral in polar coordinates. Do not evaluate the integral in this part. Be sure to...
Si U=(x2+y2+z2)-1/2 , demuestre que ∂2U/∂x2+∂2U/∂y2+∂2U/∂z2=0
Si U=(x2+y2+z2)-1/2 , demuestre que ∂2U/∂x2+∂2U/∂y2+∂2U/∂z2=0
Solve the following equations in non-negative integers. 1. x2 - y2 = 221 2. a +...
Solve the following equations in non-negative integers. 1. x2 - y2 = 221 2. a + b = ab 3. gcd(a,b)lcm(a,b) = b + 9 4. x4 + 2x3 - y2(1+2x) + x2(1-y2) = 2299
Show that the set ℝ2R2, equipped with operations (?1,?1)+˜(?2,?2)=(?1+?2+1,?1+?2−1)(x1,y1)+~(x2,y2)=(x1+x2+1,y1+y2−1) ? ⋅˜ (?,?)=(??+?−1,??−?+1) (1)defines a vector space...
Show that the set ℝ2R2, equipped with operations (?1,?1)+˜(?2,?2)=(?1+?2+1,?1+?2−1)(x1,y1)+~(x2,y2)=(x1+x2+1,y1+y2−1) ? ⋅˜ (?,?)=(??+?−1,??−?+1) (1)defines a vector space over ℝR. (2)Show that the vector space ?V defined in question 1 is isomorphic to ℝ2R2 equipped with its usual vector space operations. This means you need to define an invertible linear map ?:?→ℝ2T:V→R2.
Find and classify all the extrema of the function f(x; y) = Exp(-x2 -y2 )*(x2 +...
Find and classify all the extrema of the function f(x; y) = Exp(-x2 -y2 )*(x2 + 2y2).
For the following exercises, graph the inequality. 1/4 x2 + y2 < 4
For the following exercises, graph the inequality.1/4 x2 + y2 < 4
Let  F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...
Let  F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j + (3 + x) k . Let a > 0  and let S be part of the spherical surface x2 + y2 + z2 = 2az + 15a2 that is above the x-y plane and the disk formed in the x-y plane by the circular intersection between the sphere and the plane. Find the flux of F outward across S.
a) Find the volume of the solid obtained by revolving the region in the first quadrant...
a) Find the volume of the solid obtained by revolving the region in the first quadrant bounded by the curves y= x^(1/2) & y= x^5 about the x-axis b) Find the volume of the solid obtained by revolving the region between the curve f(x)= x^(1/3) , the line y=2, and the line x=8 about the y-axis
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT