grandes-ecoles 2013 QIII.D.4

grandes-ecoles · France · centrale-maths1__pc Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution
Deduce $\int _ { 0 } ^ { \pi } \ln \left( x ^ { 2 } - 2 x \cos \theta + 1 \right) \mathrm { d } \theta$ for $x \in \mathbb { R } \backslash \{ - 1,1 \}$. 
Deduce $\int _ { 0 } ^ { \pi } \ln \left( x ^ { 2 } - 2 x \cos \theta + 1 \right) \mathrm { d } \theta$ for $x \in \mathbb { R } \backslash \{ - 1,1 \}$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QII.A.1 QII.A.2 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C.1 QII.C.2 QII.C.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.B.5 QIII.B.6 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.D.1 QIII.D.2 QIII.D.3 QIII.D.4 QIII.D.5 QIII.D.6 QIII.D.7 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B QIV.C.1 QIV.C.2