Question
Question: If \(\int _ { 0 } ^ { k } \frac { d x } { 2 + 8 x ^ { 2 } } = \frac { \pi } { 16 }\) then \(k =\)...
If ∫0k2+8x2dx=16π then k=
A
1
B
21
C
41
D
None of these
Answer
21
Explanation
Solution
∫0k2+8x21dx=21∫0k1+(2x)2dx=41∫02k1+t2dt
.
Comparing it with the given value, we get
tan−12k=4π⇒2k=1⇒k=21.