MA1014_HW8r_201012

MA1014_HW8r_201012 - Maths II - Homework 8 – Integration...

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Unformatted text preview: Maths II - Homework 8 – Integration by trigonometric substitution Instruction: Solve only the EVEN problems from the following list: Integral 1.2.Answer ∫ ∫ 1− x2 dx x2 dx x 2 − 36 −sen −1 x − 1− x2 +c x ln x + x 2 − 36 + C € € 3.4.5.6.- ∫ ∫x ∫ 4 + x 2 dx 3 € € ( ) 1 − x 2 dx dx 3 2 € € € € € (x 2 − 4) x 4 + x 2 + 2 ln 4 + x 2 + x + C 2 3 5 1 1 − (1 − x 2 ) 2 + (1 − x 2 ) 2 + C 3 5 1 x − +C 4 x2 − 4 3 12 x + 7) 2 + C ( 3 ȹ x ȹ sen −1ȹ ȹ + C ȹ 5 Ⱥ ∫x ∫ ∫ ∫ x 2 + 7 dx dx 25 − x 2 dx € 7.- € 8.€ € € x 16 − x 2 dx x 1+ x2 14 16 − x 2 ln − +C 4x x ln 1+ x2 1 − +C x x 3 22 9.€ 10.€ ∫ ∫ ∫ 1− x2 dx x4 x2 3 € € −(1 − x 3x x 3 ) +c 11.- dx € 12.€ € (9 − x 2 ) 2 dx (1 + x ) dx 22 ȹ x ȹ − sen −1ȹ ȹ + c ȹ 3 Ⱥ 9 − x2 1 1x arctan x + +C 2 2 1+ x2 1 x 1 x3 − 3 +C 16 4 + x 2 48 22 (4 + x ) € € € 13.- ∫ ∫ (4 + x ) 2 5 22 14.- dx x + 2 x + 10 ln € x 2 + 2 x + 10 x + 1 + +C 3 3 € € € fpm@itesm.mx Maths II - Homework 8 – Integration by trigonometric substitution 15.16.€ ∫ dx (x 2 + 6 x + 13) 2 1 x+3 ( x + 3) + tan−1 +C 2 16 2 8( x + 6 x + 13) ∫ x−3 (5 − 4 x − x ) 3 22 dx € € € −5 x − 1 9 5 − 4x − x2 +C 17.18.19.20.- ∫x ∫ 1 −1 5 € 2x + 4 dx 2 + 4 x + 13 x2 dx x 2 + 16 ln x 2 + 4 x + 13 + c € € ∫ 0 4 − x dx dx € 3 2 2 ȹ x ȹ x − 4 tan−1ȹ ȹ + c ȹ 4 Ⱥ 2 3+ π 3 ∫ € (x 2 + 25) 2 50 € € € fpm@itesm.mx ...
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This note was uploaded on 12/26/2010 for the course MT 1014 taught by Professor Franciscoperez during the Fall '10 term at ITESM.

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