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Evaluate the definite integral:
`int_0^2 (6x +3)/(x^2 + 4)` dx
Concept: undefined >> undefined
Evaluate the definite integral:
`int_0^1 (xe^x + sin (pix)/4)`
Concept: undefined >> undefined
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`int_1^(sqrt3)dx/(1+x^2) ` equals:
Concept: undefined >> undefined
`int_0^(2/3) dx/(4+9x^2)` equals:
Concept: undefined >> undefined
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3
Concept: undefined >> undefined
Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by x2 - y2 = cx
Concept: undefined >> undefined
Find the equations of the tangent and the normal, to the curve 16x2 + 9y2 = 145 at the point (x1, y1), where x1 = 2 and y1 > 0.
Concept: undefined >> undefined
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`
Concept: undefined >> undefined
Form the differential equation of the family of curves represented by y2 = (x − c)3.
Concept: undefined >> undefined
Form the differential equation corresponding to y = emx by eliminating m.
Concept: undefined >> undefined
Form the differential equation from the following primitive where constants are arbitrary:
y2 = 4ax
Concept: undefined >> undefined
Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c2 + c3
Concept: undefined >> undefined
Form the differential equation from the following primitive where constants are arbitrary:
xy = a2
Concept: undefined >> undefined
Form the differential equation from the following primitive where constants are arbitrary:
y = ax2 + bx + c
Concept: undefined >> undefined
Find the differential equation of the family of curves y = Ae2x + Be−2x, where A and B are arbitrary constants.
Concept: undefined >> undefined
Find the differential equation of the family of curves, x = A cos nt + B sin nt, where A and B are arbitrary constants.
Concept: undefined >> undefined
Form the differential equation corresponding to y2 = a (b − x2) by eliminating a and b.
Concept: undefined >> undefined
Form the differential equation corresponding to y2 − 2ay + x2 = a2 by eliminating a.
Concept: undefined >> undefined
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
Concept: undefined >> undefined
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x + a)2 + y2 = a2
Concept: undefined >> undefined
