The distance between the X-axis and the point (3, 12, 5) is
3
13
14
12
If f(x) = ∫1xsin2t2dt, then the value of limx→0fπ + x - fπx is equal to
34
1
∫1x2x4 + 134dx is equal to
- 1 + x434x + C
- 1 + x4142x + C
- 1 + x414x + C
- 1 + x414x2 + C
∫1 + xexsin2xexdx is equal to
- cotex + C
tanxex + C
tanex + C
- cotxex + C
∫xex1 + x2dx is equal to
- exx + 1 + C
exx + 1 + C
xexx + 1 + C
- xexx + 1 + C
∫exsinx + 2cosxsinxdx is equal to
excosx + C
exsinx + C
exsin2x + C
∫1 + cosxdx is equal to
2sinx2 + C
12sinx2 + C
22sinx2 + C
∫x2 - 1xdx is equal to
x2 - 1 - sec-1x + C
x2 - 1 + tan-1x + C
x2 - 1 + sec-1x + C
x2 - 1 - tanx + C
∫5 + x2x4dx is equal to
1151 + 5x232 + C
- 1151 + 1x232 + C
- 1151 + 5x232
1151 + 1x232
The value of ∫01dxex + e is equal to
1elog1 + e2
log1 + e2
1elog1 + e
log21 + e
A.
Let I = ∫01dxex + e = ∫01dxex1 + eexPut 1 + eex = t ⇒ 0 - eexdx = dt⇒ 1exdx = - 1edt∴ I = - 1e∫1 + e21tdt = - 1elogt1 + e2 = - 1elog2 - log1 + e = - 1elog21 + e
= 1elog1 + e2