Compute the integral along the arc of the parabola x = y2 from (1,-1) to (1,1)
Evaluate the integral taken along the quarter circle x = cos t, y = sin t, joining the same points.
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By changing the order of integration, the integral can be represented as determine the value of A.
Evaluate over the positive quadrant of the circle x2 + y2 = 1 .
Let R be the image of the triangular region S with vertices (0, 0) (0,1) is uv-plane under the transformation x = 2u - 3v and y = u + v.
Then equals
over the semicircle x2 + y2 = ax in the positive quadrant is equal to -
An integrating factor for the differential equation (cos y sin 2x) dx + (cos2y - cos2x ) dy = 0 is,
Let then, which of the follwing is not true ?
Let y(x) be the solution of initial value problem,
The y(1) is equal to,
Let F(x) be the particular integral of the differential equation y" + y = (x - cot x) If there exist c e R such that F(c) = c, then c is equal to,
Let y(x) be the solution of the differential equation,
Satisfying the condition Then which o f the following is/are
If f(x) is defined [ -2,2 ] by / ( x ) = 4x2 - 3x +1 and then
If the equation of the curve is x2 + y2 = a2 then
Evaluate where S is the entire surface of the solid bounded by the cylinder x2 + y2 =1 and the planes z = 0, z = x + 2.
The value of over the area between the parabola y - x2 and the line y = x is ______.
Evaluate the integral over the volume enclosed by three coordinate planes and the plane x + y + z = 1.
Evaluate over the domain {(x, y ) : x ≥ 0, y ≥ 0, x2 + y2 ≤ 1}.
If the orthogenal trajectories of the family of ellipse 9x2 + 4y2 = c1 where c1 > 0 are given by where c2 ∈ R , then the value of β i s ..... ( conect upto two decimal places).
Consider the differential equation y" + 4y = 8cos2x , with y(0) = 0 and then y( π ) is equal to _________ .
Let y(x) = c1 f(x) + c2 g(x) be the general solution of (x + 2) y" - (4x + 9)y' + (3x + 7)y = 0, then f(0) + g(0) is equal to _________.
Consider the differential equation then y(e) is equal to
Let y(x) is a solution of differential equation equal to. satisfying y(o) = 1. then
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