( 3)  x 2 sin   ( 1 x x x 3 2 19. 2) x x 0 1 dx 2 1) 20. dx ( 2 3 18. 2 8. cos x xdx 0 5  3 1 x e 9. 0 dx 2 10. 7 3  x dx 3 xdx 11. 2 0 2 70 Summary You have learnt the following from this chapter: a). The fundamental Theorem of the Integral calculus If then b ( ) (b ) ( )  f x dx G G a a b b). can be defined as the area enclosed by the four boundaries y = f(x), a the x- axis and the ordinates x = a and x = b. Further Reading i).Additional Pure mathematics Harwood Clarke Heinemann Educational Books Ltd London
x 3  2 x 2  sin x 0 dx 18. 19. 20. 3 ( x 1) 2 ( x 2) 1 2 1 ( x  3) dx 8. 2 x cos xdx 0 9. 1 e 0 5 x  3 dx 10. 2 7 x  3 dx 11. 2 0 2 3 xdx 70 Summary You have learnt the following from this chapter: a). The fundamental Theorem of the Integral calculus If then b f ( x ) dx  G (b ) G ( a ) a b b). can be defined as the area enclosed by the four boundaries y = f(x), a the x- axis and the ordinates x = a and x = b. Further Reading i).Additional Pure mathematics Harwood Clarke Heinemann Educational Books Ltd London
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