Solve (1 + y2)dx = (tan-1y - x)dy
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Identify the nature of singular points of the differential equation x2(x - 2)y" + (x - 1)y' + 2xy = 0
For any two real numbers a and b (a < b) prove that a2+ ab+ b2 = 3c2,for some c ∈ (a,b) using Lagrange's mean value theorem.
Solve equation y= 3x + loge p
Using Maclaurin's series expand tan x up to the term containing x5
Find the volume of sphere x2 + y2 + z2 = a2 using triple integrals.
Find the volume bounded by xy- plane, the cylinder x2+y2= 1 and the plane x+y+z = 3
Find the volume in the positive octant bounded by the plane x+2y+3z =4 and the coordinate planes.
A circular hole of radius b is made centrally through a sphere of radius a . Find the volume of remaining sphere.
Find the centroid of the upper half of the circle x2+y2= a2
Find the area bounded between the curve y2= 4x and x2= 4y using Green's theorem.
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