CATHOLIC JUNIOR COLLEGE MATHEMATICS DEPARTMENT 2020 JC2 H2 MATHEMATICS TIMED ASSESSMENT – DEFINITE INTEGRALS Duration: 45 mins Name: _________________________ Home Tutorial Class: _______ Date: ______________ Instructions: (1) Answer all questions. (2)Give non-exact numerical answers correct to 3 significant figures, unless a different level of accuracy is specified in the question. Q1.By using the substitution 1ux, find the exact value of 301dxxx.  Solution: 211uxuxdd212dduxuuxu33 1200 122124212531d1d1dd12 d2d253328112535311615xxxxuuuuuuu uuuuuu25
Q2. With origin O, the curves with equations sinyxand cosyx, where 120πx, meet at the point Pwith coordinates 112π,42. (i)Find the exact area of the region bounded by the curves and the y-axis.  (ii)The region bounded by cosyx, the line π4xand the x-axis is rotated about the x-axis through360. Find the exact volume.