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14 Techniques of Integration

14 Techniques of Integration - 14 1 (a[5marks/6 0 sin 3 2 x...

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14. TECHNIQUES OF INTEGRATION 1. Evaluate the following integrals. (a) [5 marks] 6 / 0 3 2 cos 2 sin π dx x x . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[5 marks] - 4 0 1 dx x . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [3 marks] 4 / 0 2 π θ θ d e i . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 81 14. Techniques of Integration
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__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 82 14. Techniques of Integration
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2. Evaluate the following integrals. (a) [4 marks] 6 / 0 sin 2 cos π dx e x x __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[3 marks] - 3 1 2 10 dx x x __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [3 marks] dx x dx d + 1 0 4 1 . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 3. (a) [2 marks] Differentiate  y  =  x  ln  x  with respect to  x . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[3 marks] Use your answer to find  dx x ln . VET: Calculus 83 14. Techniques of Integration
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__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 84 14. Techniques of Integration
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4. Find the following integrals. (a) [4 marks] - + dx x x x x 2 2 3 ) ( sin π π π __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[4 marks] + + + dx x x x 9 6 12 4 2 __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [4 marks] + dx ) x ( e e x x 1 3 2 3 __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (d)[4 marks] π θ θ 0 4 6 d e i  giving your answer in cartesian form. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 85 14. Techniques of Integration
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__________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 86 14. Techniques of Integration
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