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Pre-Calc Homework Solutions 253

# Pre-Calc Homework Solutions 253 - Section 6.3 15 Use...

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Unformatted text preview: Section 6.3 15. Use tabular integration with f (x) f(x) and its derivatives x2 2x 2 0 (+) () (+) g(x) and its integrals sin 2x 253 x 2 and g(x) sin 2x. 1 cos 2x 2 1 sin 2x 4 1 cos 2x 8 x 2 sin 2x dx 1 /2 0 1 2 x cos 2x 2 1 x sin 2x 2 x sin 2x 2 1 cos 2x 4 C 2x 2 cos 2x 4 1 C x 2 sin 2x dx 2x 2 cos 2x 4 2 x /2 sin 2x 2 0 1 2 4 2 ( 1) 0 1 (1) 4 0 2 8 1 2 0.734 Check: NINT x 2 sin 2x, x, 0, 2 0.734 x 3 and g(x) cos 2x. 16. Use tabular integration with f (x) f(x) and its derivatives x3 3x2 6x 6 0 (+) () (+) () g(x) and its integrals cos 2x 1 sin 2x 2 1 cos 2x 4 1 sin 2x 8 1 cos 2x 16 x 3 cos 2x dx 1 3 x sin 2x 2 x3 2 3 2 x cos 2x 4 3x 2 4 3x 2 4 3 x sin 2x 4 3 cos 2x 8 3 cos 2x 8 3x sin 2x 4 x3 2 3x sin 2x 4 3 2 16 3 2 16 C /2 0 x 3cos 2x dx 0 3 4 3 /2 cos 2x 8 0 3 (1) 8 3 ( 1) 8 0 1.101 1.101 Check: NINT x 3cos 2x, x, 0, 2 ...
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