Tutorial 12 - 19 xdx e x 4 sin 20 xdx x 2 cos cos In...

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Tutorial 12 – Introduction to Calculus and Linear Algebra Page 1 of 1 Tutorial 12 Introduction to Calculus and Linear Algebra In Exercises 1 to 20, find the indicated integral. Check your answers by differentiation. 1. - - dy y y ) 2 3 ( 3 2. + dx x x e x 2 3. - du u u 1 3 1 1 . 1 4. + + dx x x x 2 2 1 2 5. - - dx x x x 5 1 ) 2 ( 2 3 6. - dt t t ) 1 ( 2 7. + dt e t 2 ) 1 ( 8. + - - dy e y y y 2 / 5 3 1 9. dx xe x 2 10. + dt t t 5 2 ) 1 ( 11. + dy y y 1 2 5 4 12. + + + dx x x x 12 2 ) 5 2 )( 1 ( 13. + + + + + dx x x x x x 12 10 5 6 12 3 4 5 3 4 14. dx x x 2 ) (ln 1 15. + + dx x x x 1 ) 1 ln( 2 2 2 16. + dx x x ) 1 ( 1 17. - dx e x x 3 2 18. xdx x ln 2
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Unformatted text preview: 19. ∫ xdx e x 4 sin 20. ∫ xdx x 2 cos cos In Exercises 21 to 25, the slope f’ ( x ) at each point ( x , y ) on a curve y = f ( x ) is given along with a particular point ( a , b ) on the curve. Use this information to find f ( x ). 21. ; 1 4 ) ( ' + = x x f (1, 2) 22. ; 2 2 ) ( ' 2 3 +-= x x x f (1, 3) 23. ; ) ( ' 2 x e x f x + =-(0, 4) 24. ; ) 2 1 ( ) ( ' 2 / 3 x x f-= (0, 0) 25. ; ) ( ' 2 4 x xe x f-= (–2, 1)...
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