tutorial 8 mths121 2019, Assignments of Computer Science

Download tutorial 8 mths121 2019 and more Assignments Computer Science in PDF only on Docsity! MTHS 121 Tutoriaal/Tutorial 8 4/09/2019 SG 6.2-6.4 1. Bepaal die volgende integrale. Determine the following integrals. (a) ∫ sin2 x cos5 x dx (b) ∫ sin2 x cos4 x dx (c) ∫ tan4 θ dθ (d) ∫ cos(5u) sinu du (e) ∫ 1 csc 2x csc 3xdx (f) ∫ 4 dx√ e6x−1 (g) ∫ 1 (h−2)(h2+4)dh (h) ∫ 2x2+3 x(x−1)2 dx (i) ∫ x4−2x2+4x+1 x3−x2−x+1 dx (j) ∫ 8x3+13x (x2+2)2 dx (k) ∫ sin3 φ cos2 φdφ (l) ∫ cos5 t 3√sin t dt (m) ∫ cot5 α csc7 αdα (n) ∫ x2 dx√ x2−6 (o) ∫ dx x √ x2+4 (p) ∫ dx x2 √ 5−x2 2. Bepaal die volgende integrale. Determine the following integrals. (a) ∫ 1 0 √ 1− x2dx (b) ∫ 2 0 dx√ 4x2+1 (c) ∫ 2 1 dx (9−x2) 3 2 (d) ∫ 2√ 3 √ x2−3 x dx (e) ∫ 4 0 k−1 k2−4k−5dk 3. Bewys die volgende. Prove the following. (a) ∫ sin3 ( x 2 ) dx = 2 3 cos3 ( x 2 ) − 2 cos ( x 2 ) + C (b) ∫ cot3 2x dx = − 1 4 cot2 2x− 1 2 ln | sin 2x|+ C (c) ∫ dx x √ 4x2+9 = 1 3 ln ∣∣∣√4x2+9−3 2x ∣∣∣+ C Hierdie tutoriaal word nie ingehandig nie. Dinsdag 1 Oktober 2019 sal daar oor hierdie tutoriaal (slegs leereenhede 6.2 en 6.3) toets geskryf word. / This tutorial doesn’t have to be submitted. Tuesday 1 October 2019 a test will be written on this tutorial (only study units 6.2 and 6.3). 1