You are watching: Evaluate the line integral, where c is the given curve.
How perform you solve this by utilizing the following parametrics? I split them up yet got a an adverse answer that -1/3. What"s wrong?
For $C_1$ got, $langle t, t/2 angle$, $0 leq t leq 2$.
For $C_2$ got, $langle t, 3-y angle$, $2 leq t leq 3$.
$$;;;(0,0) o(2,1),:;;; 0le xle 2;,;;y=frac x2implies$$
$$intlimits_(0,0)^(2,1)(x+2y)dx+x^2dy=intlimits_0^2 (x+x)dx+x^2left(frac12,dx ight)=intlimits_0^2left(frac12x^2+2x ight)dx=$$
and something similar with the other one...
See more: How Far Is Seguin From San Antonio, Tx To Seguin, Tx, Distance From San Antonio, Tx To Seguin, Tx
$$(2,1) o(3,0):;;;2le xle 3;,;;y=-x+3implies$$
$$intlimits_(2,1)^(3,0(x+2y)dx+x^2dy=intlimits_2^3 (x+2(-x+3))dx+x^2left((-1),dx ight)=intlimits_2^3left(-x^2-x+6 ight)dx=$$
$$left.-frac13x^3 ight|_2^3-left.left.frac12x^2 ight|_2^3+6x ight|_2^3=-frac193-frac52+6=-frac176$$
edited Apr 30 "13 in ~ 21:05
reply Apr 30 "13 at 20:56
203k1717 yellow badges116116 silver- badges269269 bronze title
include a comment |
Try writing these integrals as$$int_C (x+2y,x^2)cdot (dx,dy)$$where $cdot$ is the usual inner product.Now, for $C_1$, make $(x,y)=(x(t),y(t))=(t,fract2)$ (if your parametrization is correct), indigenous which we have $dx=dt$ and also $dy=fracdt2$. You have the right to now easily integrate with respect come $t$, within the range where $t$ varies.
answered Apr 30 "13 in ~ 20:50
4,4941919 silver badges5454 bronze badges
add a comment |
Not the price you're looking for? Browse various other questions tagged multivariable-calculus or asking your very own question.
Featured ~ above Meta
How do you advice this line integral, where C is the offered curve?
exactly how do you evaluate this line integral, whereby C is the provided curve?
advice the heat integral $int_C x^2 dx+(x+y)dy $
advice a line integral making use of the fundamental theorem of line integrals
evaluate the heat integral offered the course of a helix?
advice the line integral provided the pathway C= C1+ C2
Evaluate line integral there is no Green's organize
evaluate integral whereby $C$ is the course of straight line segments in 3D
hot Network questions more hot concerns
ridge Exchange Network
site style / logo design © 2021 ridge Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.19.40496