11X1 T17 02 definite integral

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1. Properties Of Definite Integral 2. Properties OfDefinite Integral n 1 b x 1 abx dx n n 1 a 3. Properties OfDefinite Integral n 1 b x 1 abx dx n n 1 a 2 a kf x dx k a f x dxb b can only factorise constants 4. Properties Of Definite Integraln 1 bx 1 ab x dx n n 1 a 2 a kf x dx k a f x dxbbcan only factorise constants 3 a f x g x dx a f x dx a g x dx b b b 5. Properties OfDefinite Integral n 1 b x 1 abx dx n n 1 a 2 a kf x dx k a f x dxb bcan only factorise constants 3 a f x g x dx a f x dx a g x dx bb b 4 a f x dx a f x dx c f x dxb c b 6. 5 a x n dx 0b 7. 5 a x n dx 0b , if f x 0 for a x b 8. 5 a x n dx 0b , if f x 0 for a x b 0, if f x 0 for a x b 9. 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 dxbb 10. 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 dxbb , if f x g x for a x b 11. 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 dxbb , if f x g x for a x b7 a f x dx b f x dxba 12. 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 b b , if f x g x for a x b7 a f x dx b f x dx b aa 8 f x 0 , if f x is odda 13. 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 b b , if f x g x for a x b7 a f x dx b f x dx b aa 8 f x 0 , if f x is odda a a 9 f x 2 f x ,if f x is evena 0 14. 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 b b , if f x g x for a x b7 a f x dx b f x dx b aa 8 f x 0 , if f x is odd NOTE :a a a odd odd even 9 f x 2 f x ,if f x is evenodd even odda even even even 0 15. 2 e.g. (i) 6 x 2 dx1 16. 22 e.g. (i) 6 x 2 dx1 x 3 61 3 1 17. 2 2 e.g. (i) 6 x 2 dx1 x 3 61 3 1 223 13 14 18. 2 2 e.g. (i) 6 x 2 dx1 x 3 61 3 1 223 13 145 ii 3 xdx0 19. 2 2 e.g. (i) 6 x 2 dx1 x 3 61 3 1 223 13 1455 1 ii 3 xdx x dx3 00 20. 2 2 e.g. (i) 6 x 2 dx 1 x 3 61 3 1 223 13 145 5 1 ii 3 xdx x dx 3 0 053 4 x 34 0 21. 2 2 e.g. (i) 6 x 2 dx 1 x 3 61 3 1 223 13 145 5 1 ii 3 xdx x dx 3 0 053 4 x 34 0 x x 03 3 54 22. 22 e.g. (i) 6 x 2 dx 1 x 3 61 3 1 223 13 1455 1 ii 3 xdx x dx3 00 5 3 4 x 3 4 0 x x 0 3 3 5 4 5 5 0 3 3 4 153 5 4 23. 2 iii sin 5 xdx2 24. 2 iii sin 5 xdx 0 odd function 5 odd function 2 25. 2 iii sin 5 xdx 0 odd function 5 odd function 21 iv x 3 2 x 2 x 1dx 1 26. 2 iii sin 5 xdx 0odd function 5 odd function 21 1 iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 10 27. 2 iii sin 5 xdx 0odd function 5 odd function 21 1 iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 10 1 2 x 3 x230 28. 2 iii sin 5 xdx 0odd function 5 odd function 21 1 iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 10 1 2 x 3 x 2 3 0 2 1 1 02 3 310 3 29. 2 iii sin 5 xdx 0odd function 5 odd function 21 1 iv x 3 2 x 2 x 1dx 2 2 x 2 1dx 10 1 2 x 3 x 2 3 0 2 1 1 02 3 310 3 Exercise 11C; 1bce, 2adf, 3ab (i, iii), 4bcf, 5, 6ac, 7df, 8b, 12b, 13*