∫cos-37xsin-117xdx is equal to:
logsin47x + c
47tan47x + c
- 74tan-47x + c
logcos37x + c
∫sinθ + cosθsin2θdθ is equal to :
logcosθ - sinθ + sin2θ
logsinθ - cosθ + sin2θ
sin-1sinθ - cosθ
sin-1sinθ + cosθ
∫π6π3dx1 + tanx is equal to :
π12
π2
3π2
2π
∫- ππsin4xsin4x + cos4xdx is equal to :
π
The value of 2sinx2sinx + 2cosxdx is :
2
π4
If f is continuous function, then :
∫- 22fxdx = ∫02fx - f- xdx
∫- 352fxdx = ∫- 610fx - 1dx
∫- 35fxdx = ∫- 44fx - 1dx
∫- 35fxdx = ∫- 26fx - 1dx
The area of the region bounded by y2 = 4ax and x2 = 4ay, a > 0 in sq unit, is :
16a23
14a23
13a23
16a2
A.
The equations of given curves arey2 = 4ax and x2 = 4ay
On solving these equations, we get
(0, 0) and (4a, 4a)
∴ Required area
= ∫04a2ax - x24adx= 2ax3232 - x312a04a= 323a2 - 16a23= 16a23 sq unit
An integrating factor of the differential equation xdydx + ylogx = xexx12logx, (x > 0) is :
xlog(x)
xlogx
elogx2
ex2
The solution of edydx = x + 1, y(0) = 3 is :
y = xlog(x) - x + 2
y = (x + 1)logx + 1 - x + 3
y = x + 1logx + 1 + x + 3
y = xlogx + x + 3
Solution of the differential equation dydxtany = sinx + y + sinx - y is :
secy + 2cosx = c
secy - 2cosx = c
cosy - 2sinx = c
tany - 2secy = c