∫π6π3dx1 + tanx is equal to
π12
π2
π6
π4
If f is a continuous function, then
∫- 22f(x)dx = ∫02f(x) - f(- x)dx
∫- 352f(x)dx = ∫- 610fx - 1dx
∫- 35fxdx = ∫- 44fx - 1dx
∫- 35fxdx = ∫- 26fx - 1dx
An integrating factor of the differential equation
xdydx + ylogx = xexx12logx, (x > 0), is
xlogx
elogx2
ex2
C.
Given differential equation is
xdydx + ylogx = xexx12logxor dydx + y . 1xlogx = ex x- 12logxHere, P = 1xlogx and Q = ex x- 12logx
∴ IF = e∫1xlogxdx = elogx22 = elogx2
Solution of the differential equation
dydxtany = sinx + y + sinx - y
secy + 2cosx = c
secy - 2cosx = c
cosy - 2sinx = c
tany - 2secy = c
Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is
1021
1113
1325
2132