HWset1 - x 2-11 x +19 (2 x +1)( x-2) dx (2) R x 2 +5 x +1 (...

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Homework 1 Due February 2, 2012 NYTI set 1(Techniques for integration I) (1) R sin( x ) dx (2) R x 5 x dx (3) R x 5 ln xdx (4) R t 0 e x sin( t - x ) dx (5) R x ln(1 + x ) dx (6) R x sec 2 (2 x ) dx (7) R x arctan xdx NYTI set 2(Techniques for integration II) (1) R tan 5 xdx (2) R cos 5 x sin x dx (3) R sin 3 ( x ) x dx (4) R x sec x tan xdx (5) R cos x +sin x sin 2 x dx (6) R 1 - tan 2 x sec 2 x dx (7) R x cos 2 xdx (8) R cos x cos 5 (sin x ) dx (9) Show R tan 3 x cos 4 x dx = tan 4 x 4 + tan 6 x 6 + c (10) R dx cos x - 1 (11) R x sec 2 ( x 2 ) tan 4 ( x 2 ) dx NYTI set 3(Techniques for integration III) (1) R 1 (5 - 4 x - x 2 ) 5 / 2 dx (2) R 1+ x 2 x dx (3) R 1 x 2 +3 x - 4 dx (4) R 40 + 6 x - x 2 dx (5) R 0 - π 2 cos x 1+sin 2 x dx NYTI set 4(Techniques for integration IV) (1) R 2
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Unformatted text preview: x 2-11 x +19 (2 x +1)( x-2) dx (2) R x 2 +5 x +1 ( x 2 +1) 2 dx (3) R 3 x 2 +18 x 2 +33 x-2 ( x 2 +6 x +10) 2 dx (4) R dx x-3 x dx (hint, make a substitution rst to express the integrand as a rational function and then evaluate the integral. To do this Let u= 6 x ) (5) R 11 ln( x 2-x + 6) dx (6) R x 2 + x +7 ( x 2 +7) 2 dx (7) R 8 7 xdx x 2-4 x-5 1...
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