Question

Evaluate ∫_0,3^2,4▒〖(2y+x^2 )dx+(3x-y)dy along〗 The parabola x=2t, y=t^2 +3 Straight lines from (0,3) to (2,3) A straight line from (0,3) to (2,4)

Answer #1

a parabola x=2t, y=t^2+3 straight lines from (0,3) to (2,3) a straight line from (0,3) to (2,4)

Find the derivatives dy/dx and d^2y/dx^2, and evaluate them at t
= 2.
x=t^2 ,y = t ln t

3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy =
0. (a) Verify this is an exact equation
(b) Solve the equation

dx
dt
= y − 1
dy
dt
= −3x + 2y
x(0) = 0, y(0) = 0

(dx/dt) = x+4z
(dy/dt) = 2y
(dz/dt) = 3x+y-3z

Given
(dy/dx)=(3x^3+6xy^2-x)/(2y)
with y=0.707 at x= 0, h=0.1 obtain a solution by the fourth
order Runge-Kutta method for a range x=0 to 0.5

Find the work done by F(x,y)= <3x^2y+1, x^3+2y> in moving
a particle from P(1,1) to Q(2,4) across the curve y=x^2. Please
explain your steps. ````

Find d^2y/dx^2 . x = t^3 − 7, y = t − t^2
d^2y/dx^2=?

find dx/dx and dz/dy
z^3 y^4 - x^2 cos(2y-4z)=4z

Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz where
C is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (Hint:
Observe that C lies on the surface z = 2xy.) C F · dr =

Evaluate the line integral:
(x^2 + y^2) dx + (5xy) dy on the edge of the circle: x^2 + y^2 = 4.
USING GREEN'S THEOREM.

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