The value of the integral ∫- π4π4sin- 4xdx is
- 83
32
83
None of these
A.
Let I = ∫- π4π4sin-4xdx= ∫- π4π41sin4xdx= ∫- π4π4csc4xdx = ∫- π4π4csc2x2dx= ∫- π4π41 + cot2xcsc2xdxPut cotx = t⇒ - csc2xdx = dt∴ I = ∫- 111 + t2dt= - 2∫011 + t2dt= - 2t + t3301= - 21 + 13= - 83
The solution of the differential equation xdy - ydx = x2 + y2dx is
x + x2 + y2 = cx2
y - x2 + y2 = cx2
x - x2 + y2 = cx
y + x2 + y2 = cx2
The differential equation of all non-vertical lines in a plane is
d2ydx2 = 0
d2xdy2 = 0
dydx = 0
dxdy = 0
∫x + 2x + 42exdx is equal to
exxx + 4 + C
exx + 2x + 4 + C
exx - 2x + 4 + C
ex2xexx + 4 + C
The value of ∫35x2x2 - 4dx
2 - loge157
2 + loge157
2 + 4loge3 - 4loge7 + 4loge5
2 - tan-157
∫0∞dxx + x2 + 13 is equal to
38
18
- 38
A common tangent to 9x2 - 16y2 = 144 and x2 + y2 = 9 is
y = 37x + 157
y = 327x + 157
y = 237x + 157
The differential equation of all parabolas whose axes are parallel to y-axis is
d3ydx3 = 0
d3ydx3+ d2xdy2 = 0
d2ydx2 + 2dydx = 0
The locus of a point P which moves such that 2PA = 3PB, where A(0, 0) and B(4,- 3) are points, is
5x2 - 5y2 - 72x + 54y + 225 = 0
5x2 + 5y2 - 72x + 54y + 225 = 0
5x2 + 5y2 + 72x - 54y + 225 = 0
5x2 + 5y2 - 72x - 54y - 225 = 0
The points P is equidistant from A(1, 3), B (- 3, 5) and C(5, - 1), then PA is equal to
5
55
25
510