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If f(t) = 0 2x dx1 - 2 t 2 x, 0 < t < , then the value of 0 2 2 dtf(t) equals .
1
x - x and add: 2f(t) = 2 0 dx1 - 2 t 2 x
f(t) = 2 0 2 dx1 - 2 t 2 x = 2 0 2 2 x dx1 + 2 t 2 x
( dividing by 2 x: 2 x - 2 t 2 x = 1 + 2 t 2 x)
Put x = z: f(t) = 2 0 dz1 + z2 2 t = 2 t 2 = 2 t
0 2 2 dtf(t) = 0 2 t dt = 1
Answer: 1
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