If a and b are unit vectors and θ is the angle between them, then the value of cosθ2 is
12a + b
12a - b
a - ba + b
a + ba - b
∫xsec2xdx is equal to
xtanx + logsecx + c
x22secx + logcosx + c
xtanx + logcosx + c
tanx + logcosx + c
∫te3t2dt is equal to
16e3t2 + c
- 16e3t2 + c
16e- 3t2 + c
- 16e- 3t2 + c
∫0πlogsin2xdx is equal to
2πloge12
πloge2
π2loge12
None of these
∫dxxxn + 1 is equal to
1nlogxnxn + 1 + c
1nlogxn + 1xn + c
logxnxn + 1 + c
A.
Let I = ∫dxxxn + 1 = ∫xn - 1dxxnxn + 1Put xn + 1 = t⇒ nxn - 1dx = dt⇒ xn - 1dx = 1ndt∴ I = 1n∫dttt - 1 = 1n∫1t - 1 - 1tdt = 1nlogt - 1 - logt = 1nlogt - 1t + c = 1nlogxnxn + 1 + c
The area bounded by the curves y2 - x = 0 and y - x2 = 0, is
7/3 sq unit
1/3 sq unit
5/3 sq unit
1 sq unit
∫02x2dx is equal to
2 - 2
2 + 2
2 - 1
- 2 - 3 + 5
Area between the curve y = cos(x) and X - axis, when 0 ≤ x ≤ 2π, is
0 sq units
2 sq units
3 sq units
4 sq units
In = ∫0π4tannxdx, then limn→∞nIn + In + 2 equals
1/ 2
4 sq uits
The order of the differential equation
ydydx = xdydx + dydx3 is
1
2
3
4