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The value of the integral 0 /4 x dx 4(2x)+ 4(2x) equals :
(3) 2 232
Put 2x=t: I= 14 0 /2 t dt 4t+ 4t
∵ 0af(t) dt= 0af(a-t) dt and the denominator does not change for t 2-t
I= 14 4 0 /2 dt 4t+ 4t
Divide by 4t and put t=y:
0 /2 4t dt1+ 4t= 0 (1+y2) dy1+y4
= 0 (1+ 1y2 )dy (y- 1y )2+2
Put y- 1y=u: = - duu2+2= 2
I= 16 2= 2 232
Answer: (3)
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