The value of ∫sin2xsin4x + cos4xdx is
tan-1cot2x + C
tan-1cos2x + C
tan-1sin2x + C
tan-1tan2x + C
The value of ∫1 + secxdx is
sin-12sinx + C
2sin-12sinx/2 + C
2sin-12sinx + C
2sin-12x/2 + C
The value of ∫x2 + 1x4 + x2 + 1dx is
13tan-1x - 1/x3 + C
123logx - 1/x - 3x - 1/x + 3 + C
tan-1x + 1/x3 + C
tan-1x - 1/x3 + C
The value of ∫01x21 - x232dx is
132
π8
π16
π32
D.
Let I = ∫01x21 - x232dxlet x = sinθ ⇒ dx = cosθdθ I = ∫0π2sin2θcos2θ32 . cosθdθ = ∫0π2sin4θ . cos4θBy Gamma function, I = Γ2 +12Γ4 + 122Γ2 + 4 + 22 = Γ32Γ522Γ4 = 12Γ . 32 . 12 . Γ122 . 3 . 2 = 3 . π . π2 . 2 . 2 . 2 . 3 . 2 = π32
The value of ∫0∞x1 + xx2 + 1dx is
2π
π4
The area of the region bounded by the curves, y2 = 8x and y = x is
643
323
163
83
If a + b + c = 0 and a = 5, b = 3 and c = 7, then angle between a and b is
π2
π3
π6
i . j × k + j . k × i + k . j × i is equal to
3
2
1
0
One card is drawn at random from a pack of playing cards the probability that it is an ace or black king or the queen of the heart will be
352
752
652
152
15 coins are tossed, then the probability of getting 10 heads will be
51132768
100132768
300332768
300532768