EXAMPLES XIV 205 



For the area B, V ox = ^((e- 1 ) 2 + {y*dx- 2(*- 2 ) 2 j 



0-9255 



EXAMPLES XIV 

 Find the values of the following definite integrals : 



(1) |(a + bx + ex 2 ) dx (2) f (a + bx + ex 2 ) dx 



Jo J-ft 



(3) (Veto (4) [e-*dx 



Jo Jo 



(5) (6) f 2" sin 2 a; da; 



Ja Jo 



(7) pcos 2 x dx (8) (V sin x dx 



Jo Jo 



(9) (V cos x dx (10) a; sin a; da; 



Jo Jo 



(11) fa; 2 sin x dx (12) P( + bx%) 2 dx 



Jo Jo 



f 4 da; 



(a + be*) dx (14 I 



} Jo Vl6 - a; 2 



(15) f-v/i 6 - a; 2 da; 



Jo 



(17) (Va; 2 + 9 da; 



o 



plO _ 



(19) I V* 2 - 25 da; 



(*3 xjU 



(21) 3- 

 J* x 



(23) The curve y = a+ for 1 ' 5 passes through the points (1, 1-82) 

 and (4, 5-32). Find a and b. Find the area under the curve 



t between x = 2 and a; = 4. 

 (24) The curve y = ad* passes through the points (2, 4-2) and 

 (8, 10-4). Find a and b. Find the area under the curve between 

 v = 4 and x = 8. 

 (25) Find the area enclosed by the line 2a; + y = 8 and the 

 curve ay =-- 4. 

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