grandes-ecoles 2013 QIII.B.4

grandes-ecoles · France · centrale-maths1__pc Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution
Show that $\int _ { 0 } ^ { \pi } \ln ( \sin \theta ) \mathrm { d } \theta = 2 \int _ { 0 } ^ { \pi / 2 } \ln ( \sin \theta ) \mathrm { d } \theta = 2 \int _ { 0 } ^ { \pi / 2 } \ln ( \cos \theta ) \mathrm { d } \theta$. 
Show that $\int _ { 0 } ^ { \pi } \ln ( \sin \theta ) \mathrm { d } \theta = 2 \int _ { 0 } ^ { \pi / 2 } \ln ( \sin \theta ) \mathrm { d } \theta = 2 \int _ { 0 } ^ { \pi / 2 } \ln ( \cos \theta ) \mathrm { d } \theta$.
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