11 x1 t16 02 definite integral (2012)

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  • 1. Properties OfDefinite Integral

2. Properties Of Definite Integraln 1 bx 1 a b x dx n n 1 a 3. Properties Of Definite Integraln 1 bx 1 a b x dx n n 1 a 2 a kf x dx k a f x dx b bcan only factorise constants 4. Properties OfDefinite Integral n 1 b x 1 a bx dx n n 1 a2 a kf x dx k a f x dx bb can only factorise constants 3 a f x g x dx a f x dx a g x dxb b b 5. Properties Of Definite Integraln 1 bx 1 a b x dx n n 1 a 2 a kf x dx k a f x dx b b can only factorise constants 3 a f x g x dx a f x dx a g x dxbb b4 a f x dx a f x dx c f x dx b c b 6. 5 a x n dx 0 b 7. 5 a x n dx 0 b, if f x 0 for a x b 8. 5 a x n dx 0 b, if f x 0 for a x b0, if f x 0 for a x b 9. 5 a x n dx 0 b, if f x 0 for a x b0, if f x 0 for a x b6 a f x dx a g x dx bb 10. 5 a x n dx 0 b, if f x 0 for a x b0, if f x 0 for a x b6 a f x dx a g x dx bb, if f x g x for a x b 11. 5 a x n dx 0 b, if f x 0 for a x b0, if f x 0 for a x b6 a f x dx a g x dx bb, if f x g x for a x b7 a f x dx b f x dx ba 12. 5 a x n dx 0b, if f x 0 for a x b 0 , if f x 0 for a x b6 a f x dx a g x dxb b, if f x g x for a x b7 a f x dx b f x dxb aa8 f x 0 , if f x is odd a 13. 5 a x n dx 0b, if f x 0 for a x b 0 , if f x 0 for a x b6 a f x dx a g x dxb b, if f x g x for a x b7 a f x dx b f x dxb aa8 f x 0 , if f x is odd aa a9 f x 2 f x ,if f x is even a 0 14. 5 a x n dx 0b, if f x 0 for a x b 0 , if f x 0 for a x b6 a f x dx a g x dxb b, if f x g x for a x b7 a f x dx b f x dxb aa8 f x 0 , if f x is odd NOTE : aa a odd odd even9 f x 2 f x ,if f x is evenodd even odd aeven even even0 15. 2e.g. (i) 6 x 2 dx 1 16. 22e.g. (i) 6 x 2 dx1 x 3 6 1 3 1 17. 2 2e.g. (i) 6 x 2 dx1 x 3 6 1 3 1 223 13 14 18. 2 2e.g. (i) 6 x 2 dx1 x 3 6 1 3 1 223 13 14 5ii 3 xdx 0 19. 2 2e.g. (i) 6 x 2 dx1 x 3 6 1 3 1 223 13 14 55 1ii 3 xdx x dx3 00 20. 2 2e.g. (i) 6 x 2 dx 1 x 3 6 1 3 1 223 13 14 5 5 1ii 3 xdx x dx 3 0 0 5 3 4 x 3 4 0 21. 2 2e.g. (i) 6 x 2 dx 1 x 3 6 1 3 1 223 13 14 5 5 1ii 3 xdx x dx 3 0 0 5 3 4 x 3 4 0 x x 0 3 3 5 4 22. 22e.g. (i) 6 x 2 dx 1 x 3 6 1 3 1 223 13 14 55 1ii 3 xdx x dx3 0053 4 x 34 0 x x 03 3 54 5 5 0 3 34153 54 23. 2iii sin 5 xdx 2 24. 2iii sin 5 xdx 0 odd function 5 odd function2 25. 2iii sin 5 xdx 0 odd function 5 odd function21iv x 3 2 x 2 x 1dx1 26. 2iii sin 5 xdx 0odd function 5 odd function21 1iv x 3 2 x 2 x 1dx 2 2 x 2 1dx10 27. 2iii sin 5 xdx 0odd function 5 odd function21 1iv x 3 2 x 2 x 1dx 2 2 x 2 1dx101 2 x3 x 2 0 3 28. 2iii sin 5 xdx 0odd function 5 odd function21 1iv x 3 2 x 2 x 1dx 2 2 x 2 1dx101 2 x3 x 2 03 2 1 3 1 0 2 3 10 3 29. 2iii sin 5 xdx 0odd function 5 odd function21 1iv x 3 2 x 2 x 1dx 2 2 x 2 1dx101 2 x3 x 2 03 2 1 3 1 0 2 3 10 3Exercise 11C; 1bce, 2adf, 3ab (i, iii), 4bcf, 5, 6ac, 7df, 8b,12b, 13*