Question

Calculus (a) Use a substitution to find the indefinite integral | (cosh^{2(x – 1)} Vcosh”[2(x – 1)} – 1) dr where r21. Show your workings. (b) Hence, calculate the definite integral ſi" (cosh" {2(x – 1)} Vcosh?{2(x – 1)} – 1) dar. Give your answer to 2 decimal places.

Answer 1

Solt Given wher x2 - 1 indefinite integal a Now have -to find the we usirg, co she - sinh'e- Coshe-1-sin he Cestetx sin(20- cost(2-1))-1- sinkhtatx-D) Then cosh'e-sine-) d sinh (2(x-))dx. t- cashi2cx- Sinheix-.2.dre dt Sinh(2x-D)dx dt Then The integral becomes Let 17 P,+S= cosisf2(x-03 t C 10

bNow have to calalate the definite integnal of we 2 From la), we have Cost fa- 10 easC)-askco] Cesh)-caso Cosh Let Than Cosh2 ete 2 et e2 2 et 2e 5 Then cosh t2) 2e R(a.718) 753,733 Ded Cosho e te 2 o153.133-] To 762. 733] 75.2133