The value of ∫ex1 + xcos2ex . xdx is equal to
- cotexx + C
tanex . x + C
tanex + C
cotex + C
The vate of ∫exx2tan-1x + tan-1x + 1x2 + 1dx is equal to
extan-1x + C
tan-1ex + C
tan-1xe + C
etan-1x + C
The value of ∫- π4π4sin103x . cos101xdx is
π4103
π4101
2
0
The value of ∫e6logx - e5logxe4logx - e3logxdx is equal to
0 + C
x33 + C
3x3 + C
1x + C
The differential coefficient of log10(x) with respect to logx(10) is
1
- log10x2
logx102
x2100
∫0π2sin1000xsin1000x + cos1000xdx is equal to
1000
π2
π4
D.
Let I = ∫0π2sin1000xsin1000x + cos1000xdx ...i⇒ I = ∫0π2sin1000π2 - xsin1000π2 - x + cos1000π2 - xdx ∵ ∫0afxdx = ∫0afa - xdx⇒ I = ∫0π2cos1000xsin1000x + cos1000xdx ...iiOn addingEqs. (i) and (ii), we get 2I = ∫0π2sin1000x + cos1000xsin1000x + cos1000xdx⇒ 2I = ∫0π21dx = x0π2 ⇒ 2I = π2∴ I = π4
The solution for the differential equation dydx + dxx = 0 is
1y + 1x = C
logxlogy = C
xy = C
x + y = C
The order and degree of the differential equation 1 + dydx2 + sindydx34 = d2ydx2
order = 2, degree = 3
order = 2, degree = 4
oreder = 2, degree = 34
order = 2, degree = not defined
If a and b are unit vectors, then what is the angle between a and b for 3a - b to be unit vector?
30°
45°
60°
90°
Suppose a + b + c = 0, a = 3, b = 5, c = 7, then the angle between a and b is
π
π3