What is ∫01x1 - x9dx = ?
1110
1132
1148
1240
A.
Let the given integral be,I = ∫01x1 - x9dxPut 1 - x = t ⇒ dx = - td andx = 1 - twhen x = 0, t = 1, and when x = 1, t = 0⇒ I = ∫101 - tt9 - dt = - ∫10 - t10 + t9dt = - ∫10 - t10 + t9dt = - t1111 + t101001 = - 111 + 110 = - 10 + 11110 = 1110
What is ∫28x - 5dx = ?
2
3
4
9
What is ∫sin3xcosxdx = ?
cos4x + c
sin4x + c
1 - sin2x24 + c
1 - cos2x24 + c
What is ∫elntanx = ?
lntanx + c
lnsecx
tanx + c
etanx + c
What is ∫ - 11ddxtan-11xdx = ?
0
- π4
- π2
π2
What is ∫dxa2sin2x + b2cos2x = ?
c + 1abtan-1atanxb
c - 1abtan-1btanxa
c + 1abtan-1btanxa
None of the above
What is ∫dxxx7 = 1 = ?
12lnx7 - 1x7 + 1 + c
17lnx2 + 1x7 + c
lnx2 - 17x + c
17lnx7x7 + 1 + c
What is ∫xe - 1 + ex - 1xe + exdx =?
x22 + c
lnx + e + c
lnxe + ex + c
1elnxe + ex + c
If xdy = y(dx + ydy); y(1) = 1 and y(x) > 0, then what is y( - 3) equal to ?
1
If f(x) and g(x) are continuous functions satisfying f(x) = f(a - x) and g(a) + g(a - x) = 2, then what is
∫0af(x)g(x)dx equal to ?
∫0agxdx
∫0afxdx
2∫ 0afxdx