If ∫0p11+4x2dx=π8, then the value of p is
14
-12
32
12
Explanation for the correct option.
Find the value of p:
Given,
∫0p11+4x2dx=π8.
Let, 2x=t
⇒2dx=dt
If x=0, then t=0 and x=p, then t=2p.
So, the integral should be,
∫02p11+t2dt=π8⇒12tan-1t02p=π8[∵∫tan-1x=11+x2]⇒tan-12p=π4⇒2p=tanπ4⇒2p=1[∵tanπ4=1]⇒p=12
Hence, the correct option is D.
If ∫a011+4x2dx=π8,then a = ............
If ∫0pdx1+4x2=π8, then the value of p is