The volume of an object expressed in spherical coordinates is given by
Q. The value of the integral is
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Consider the shaded triangular region P shown in the figure. What is xy dxdy?
Changing the order of integration in the double integral leads to, then the value of q is
dxdy over the positive quadrant of the circle x2 + y2 = 1 is given by
The volume of the cylinder x2 + y2 = a2 bounded below by z = 0 and bounded above by z = h is given by
If A is the region bounded by the parabolas y2 = 4x and x2 = 4y, then is equal to
If A is the region bounded by the parabolas y2 = 4x and x2 = 4y, then dxdy is equal to
The area of the lemniscate r2 = a2 cos2θ is given by
The area bounded by the curves y2 = 9x, x —y + 2 = 0 is given by
The area of the cardioid r = a (1 + cosθ) is given by
The area bounded by the curves y = 2√x, y = - x, x = 1 and x = 4 is given by
The area o f the region bounded by the curve y(x2 + 2 ) = 3x and 4y = x2 is given by
The area bounded by the curve r = θ cosθ and the lines θ = 0 and θ = π/2 is given by
The solution of the differential equation dy/dx = x log x is