Question

Show that $\frac { \pi ^ { 2 } } { 12 }$

• A. $\frac { \pi ^ { 2 } } { 12 }$
• B. $\frac { \pi ^ { 2 } } { 6 }$
• C. –$\frac { \pi ^ { 2 } } { 6 }$
• D. –$\frac { \pi ^ { 2 } } { 12 }$

Answer 1

Answer: (D)

–$\frac { \pi ^ { 2 } } { 12 }$

Answer 2

Let I = dx

Integrating by parts taking ln x as first function, we have

= – dx

I = 0 – dx

= –dx

= – dx

= –

= – $\left( 1 - \frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { 3 ^ { 2 } } - \frac { 1 } { 4 ^ { 2 } } + \ldots \right)$

= – $\frac { \pi ^ { 2 } } { 12 }$