# Tutorial 13 - Tutorial 13 Introduction to Calculus and...

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Tutorial 13 – Introduction to Calculus and Linear Algebra Page 1 of 1 Tutorial 13 Introduction to Calculus and Linear Algebra In Exercises 1 to 8, find the indicated integral. 1. + + 1 0 3 4 ) 1 3 ( dx x x 2. + + 3 1 2 1 1 1 dx x x 3. - - + 1 3 3 1 dt t t 4. - 2 1 4 ) 4 2 ( dx x 5. + + + 1 0 2 4 3 1 2 ) ( dx x x x x 6. + - 1 2 1 e dx x x 7. dx x x e 2 1 2 ) (ln 8. 2 / 1 3 / 1 2 / 1 dx x e x In Exercises 9 to 11, find the area of the region R that lies under the given curve y = f ( x ) over the indicated interval a < x < b . 9. Under 4 x y = , over –1 < x < 2 10. Under x e y 2 = , over 0 < x < ln 3 11. Under 2 / 1 ) 4 3 ( + = x y , over 0 < x < 4 In Exercises 12 to 15, find the area of the region R . 12. R is the region bounded by the lines y = x , y = – x , and x = 1. 13. R is the region bounded by the x axis and the curve 3 4 2 - + - = x x y . 14. R is the region bounded by the curve x x y 2 2 - = and the x axis. 15. R is the region bounded by the curves x x y 2 2 - = and 4 2 + - = x y . In Exercise 16 to 21, solve the first order ordinary differential equations.
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