If a = i^ + j^ + k^, b = 2i^ - 4k^ and c = i^ + λj^ + 3k^ are coplanar, then the value of λ, is
5/2
3/5
7/3
None of these
∫1 - x1 + xdx is equal to
cos-1x + 1 - xx - 2 + c
cos-1x - 1 - xx - 2 + c
cos-1x + 1 - xx + 2 + c
None of the above
∫logx + 1 + x21 + x2dx is equal to
12logx + 1 + x22 + c
logx + 1 + x22 + c
logx + 1 + x2 + c
∫sin8x - cos8x1 - 2sin2xcos2xdx is equal to
sin2x + c
- 12sin2x + c
12sin2x + c
- sin2x + c
∫dxsinx + sin2x is equal to
16log1 - cosx + 12loglog1 + cosx - 23log1 + 2cosx + c
6log1 - cosx + 2loglog1 + cosx - 23log1 + 2cosx + c
6log1 - cosx + 12loglog1 + cosx + 23log1 + 2cosx + c
A.
Let I = ∫dxsinx + sin2x = ∫dxsinx + 2sinxcosx = ∫dxsinx1 + 2cosx = ∫sinxdx1 - cosx1 + cosx1 + 2cosxPut cosx = t and sinxdx = - dt∴ I = - ∫dt1 - t1 + t1 + 2t = - ∫161 - t - 121 + t + 431 + 2tdt = - - 16log1 - t - 12log1 + t + 46log1 + 2t + c = 16log1 - cosx + 12loglog1 + cosx - 23log1 + 2cosx + c
∫fxg''x - f''xgxdx is equal to
fxg'x
f'(x)g(x) - f(x)g'(x)
f(x)g'(x) - f'(x)g(x)
f(x)g'(x) + f'(x)g(x)
Correct value of ∫0πsin4xdx is
8π3
2π3
4π3
3π8
∫0π2logsinxdx is equal to
- π2log2
πlog12
- π2log12
log2
∫0πcos3xdx is equal to
- 1
0
1π
1
The measurement ofthe area bounded by the coordinate axes and the curve y = loge(x), is
2
3
∞