∫0πxdxa2cos2x + b2sin2xdx is equal to
π2ab
πab
π22ab
The differential equation for which sin-1(x) + sin-1(y) = c is given by
1 - x2dy + 1 - y2dx = 0
1 - x2dx + 1 - y2dy = 0
1 - x2dx - 1 - y2dy = 0
1 - x2dy - 1 - y2dx = 0
∫ex1 + sinx1 + cosxdx is equal to
exsec2x2 + c
extanx2 + c
exsecx2 + c
extanx + c
∫1 + sinx4dx is equal to
8sinx8 + cosx8 + C
8sinx8 - cosx8 + C
8cosx8 - sinx8 + C
18sinx8 - cosx8 + C
∫0∞xdx1 + x1 + x2 is equal to
π2
0
1
π4
If In = ∫logxndx, then In + nIn - 1 is equal to
xlogxn
nlogxn
logxn - 1
The area included between the parabolas x2 = 4y and y2 = 4x is (in square units)
43
13
163
83
C.
y2 = 4x ...ix2 = 4y ...iiFrom Eqs. (i) and (ii), we get x242 = 4x⇒ x4 - 64x = 0⇒ xx3 - 43 = 0∴ x = 0, x = 4∴ Required area = ∫044xdx - ∫04x24dx= 223x3204 - 14x3304= 323 - 163 = 163 sq unit