final-sample

# final-sample - Math 1B Sample Final Examination Some...

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Unformatted text preview: Math 1B Sample Final Examination Some Formulas 1. sin 2 x = 1 2 (1- cos2 x ) 3. sin A cos B = 1 2 sin( A- B )+sin( A + B ) 2. cos 2 x = 1 2 (1 + cos2 x ) 4. sin A sin B = 1 2 cos( A- B )- cos( A + B ) 5. cos A cos B = 1 2 cos( A- B )+cos( A + B ) 6. Z tan udu = ln | sec u | + C 7. Z sec udu = ln | sec u + tan u | + C 8. Z tan n udu = 1 n- 1 tan n- 1 u- Z tan n- 2 udu 9. Z sec n udu = 1 n- 1 tan u sec n- 2 u + n- 2 n- 1 Z sec n- 2 udu 10. Weierstrass substitution: t = tan ( x 2 ) ; sin x = 2 t 1+ t 2 , cos x = 1- t 2 1+ t 2 , dx = 2 1+ t 2 dt . 11. Binomial series: (1 + x ) k = ∞ X n =0 k n x n , k n = k ( k- 1) ··· ( k- n + 1) n ! ( n ≥ 1); k = 1 12. ln(1- x ) =- x- x 2 2- x 3 3- ... . 13. arctan x = x- x 3 3 + x 5 5- x 7 7 + ... . 1. (35 points) Find: (a). Z 2 p x 2 + 4 dx (b). Z e 1 (ln x ) 2 dx (c). Z 1 / 2 arctan x x dx 2. (12 points) If the curve y = √ 2 x- x 2 , 0 ≤ x ≤ 1, is rotated about the x-axis, find the area of the resulting surface....
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## This note was uploaded on 03/25/2011 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at Berkeley.

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final-sample - Math 1B Sample Final Examination Some...

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