The equation of one of the curves whose slope at any point is equal to y + 2x is
y = 2(ex + x - 1)
y = 2(ex - x - 1)
y = 2(ex - x + 1)
y = 2(ex + x + 1)
The area enclosed by y = 3x - 5y = 0, x = 3 and x = 5 is
12 sq units
13 sq units
sq units
14 sq units
The area bounded by the parabolas y = 4x2, and the line y = 2 is
sq units
sq units
sq units
sq units
The slope at any point of a curve y = f(x) is given by = 3x2 and it passes through (-1, 1). The equation of the curve is
y = x3 + 2
y = - x3 - 2
y = 3x3 + 4
y = - x3 + 2
The area enclosed between the curve y = 1 + x2, the y-axis and the straight line y = 5 is given by
unit
unit
5 sq unit
The area between the curve y = 2x4 - x2, the X-axis and the ordinates of two minima of the curve is
7/120
9/120
11/120
13/120
A.
7/120
We have,
y = 2x4 - x2
It can be easily seen that y is minimum for x = ± 1/2
Thus, required area A is given by
A =
The value of the parameter a such that the area bounded by y = a2x2 + ax + 1, coordinate axes and the line x = 1 attains its least value is equal to
- 1