1. 2020 JC2 H2 Math Timed Assessment_Definite Integrals.pdf...

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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 1 u x , find the exact value of 3 0 1 d x x x . [4] Solution: 2 1 1 u x u x d d 2 1 2 d d u x u u x u 3 3 1 2 0 0 1 2 2 1 2 4 2 1 2 5 3 1 d 1 d 1 d d 1 2 d 2 d 2 5 3 32 8 1 1 2 5 3 5 3 116 15 x x x x u u u u u u u u u u u u u 25
Q2. With origin O , the curves with equations sin y x and cos y x , where 1 2 0 π x , meet at the point P with coordinates 1 1 2 π, 4 2 . (i) Find the exact area of the region bounded by the curves and the y -axis. [3] (ii) The region bounded by cos y x , the line π 4 x and the x -axis is rotated about the x -axis through 360 . Find the exact volume.

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