11 x1 t16 02 definite integral (2013)

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1. Properties Of Definite Integral 2. Properties Of Definite Integral 1 abn 1bx x dx n 1 a n 3. Properties Of Definite Integral 1 abn 1bx x dx n 1 a n2 a kf x dx k a f x dx bbcan only factorise constants 4. Properties Of Definite Integral 1 abn 1bx x dx n 1 a n2 a kf x dx k a f x dx bbcan only factorise constants 3 a f x g x dx a f x dx a g x dx bbb 5. Properties Of Definite Integral 1 abn 1bx x dx n 1 a ncan only factorise constants 2 a kf x dx k a f x dx bb3 a f x g x dx a f x dx a g x dx bbb4 a f x dx a f x dx c f x dx bcb 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 b0, if f x 0 for a x b , if f x 0 for a x b 9. 5 a x n dx 0 b, if f x 0 for a x b , if f x 0 for a x b06 a f x dx a g x dx bb 10. 5 a x n dx 0 b, if f x 0 for a x b , if f x 0 for a x b06 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 b , if f x 0 for a x b06 a f x dx a g x dx bb7 a f x dx b f x dx ba, if f x g x for a x b 12. 5 a x n dx 0 b, if f x 0 for a x b , if f x 0 for a x b06 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 ba8 f x 0 , aaif f x is odd 13. 5 a x n dx 0 b, if f x 0 for a x b , if f x 0 for a x b06 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 baa8 f x 0 , a aaa0if f x is odd9 f x 2 f x ,if f x is even 14. 5 a x n dx 0 b, if f x 0 for a x b , if f x 0 for a x b06 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 baa8 f x 0 , a aaa0if f x is odd9 f x 2 f x ,if f x is evenNOTE : odd odd even odd even odd even even even 15. 2e.g. (i) 6 x 2 dx 1 16. 2e.g. (i) 6 x 2 dx 121 x 3 6 3 1 17. 2e.g. (i) 6 x 2 dx 121 x 3 6 3 1 223 13 14 18. 2e.g. (i) 6 x 2 dx 15ii 3 xdx 021 x 3 6 3 1 223 13 14 19. 2e.g. (i) 6 x 2 dx 121 x 3 6 3 1 223 13 1455001 3ii 3 xdx x dx 20. 2e.g. (i) 6 x 2 dx 121 x 3 6 3 1 223 13 1455001 3ii 3 xdx x dx 53 x 4 0 4 3 21. 2e.g. (i) 6 x 2 dx 121 x 3 6 3 1 223 13 1455001 3ii 3 xdx x dx 53 x 4 0 3 3 5 x x 0 4 4 3 22. 2e.g. (i) 6 x 2 dx 121 x 3 6 3 1 223 13 1455001 3ii 3 xdx x dx 53 x 4 0 3 3 5 x x 0 4 3 3 5 5 0 4 153 5 4 4 3 23. 2iii sin 5 xdx 2 24. 2iii sin 5 xdx 0 2odd function 5 odd function 25. 2iii sin 5 xdx 0 21iv x 3 2 x 2 x 1dx 1odd function 5 odd function 26. 2iii sin 5 xdx 0odd function 5 odd function21110iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 27. 2iii sin 5 xdx 0odd function 5 odd function21110iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 1 2 x3 x 2 0 3 28. 2iii sin 5 xdx 0odd function 5 odd function21110iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 1 2 x3 x 2 0 3 2 1 3 1 0 2 3 10 3 29. 2iii sin 5 xdx 0odd function 5 odd function21110iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 1 2 x3 x 2 0 3 2 1 3 1 0 2 3 10 3Exercise 11C; 1bce, 2adf, 3ab (i, iii), 4bcf, 5, 6ac, 7df, 8b, 12b, 13*