The regression coefficient of y on x is 2/3 and that of x on y is 4/3. The acute angle between the two regression lines is tan-1(k), where k is equal to :
19
29
118
13
∫ex - e- xex + e- xlogcoshx is equal to :
logtanhx
2logex + e- x + c
2logex - e- x + c
loglogcoshx + c
∫- 1212cosxlog1 + x1 - xdx = k . log2, then k equals to
0
- 1
- 2
12
∫0π2cosθ4 - sin2θdθ is equal to :
π2
π6
π3
π5
If f(x) = cosx - cos2x + cos3x - ... to ∞, then ∫fxdx equals to
tanx2 + c
x + tanx2 + c
x - 12tanx2 + c
x - tanx2 + c
∫01xdxx + 1 - x21 - x2 is equal to :
1
π4
π22
C.
Let I = ∫01xdxx + 1 - x21 - x2Put x = sinθ ⇒ dx = cosθdθ∴ I = ∫0π2sinθ . cosθdθsinθ + cosθ . cosθ⇒ I = ∫0π2sinθsinθ + cosθdθ ...i⇒ I = ∫0π2sinπ2 - θsinπ2 - θ + cosπ2 - θdθ⇒ I = ∫0π2cosθsinθ + cosθdθ ...ii 2I = ∫0π2sinθ + cosθsinθ + cosθdθ = ∫0π21dθ = π2⇒ I = π4
The value of ∫02afxdxfx + f2a - x is :
f(a)
f(2a)
f(0)
a
The value of ∫- π4π4x3sin4xdx is equal to :
π8
For any positive integer n, ∫dxxn + 1 + x is equal to :
1nlogexn + 1 + c
1nloge1xn + 1 + c
1nlogexxn + 1 + c
1nlogexnxn + 1 + c
∫cos2cot-11 - x1 + xdx is equal to :
12x2 + c
12sin2cot-11 - x1 + x + c
- 12x2 + c
12x + c