Let f(x) = x3 3 - x2 dx. If 5f( 2) = -4, then f(1) is equal to
(1) - 6 25
Put 3 - x2 = t ⇒ -2x dx = dt, x2 = 3 - t
f(x) = x2 3 - x2 x dx = - 12 (3 - t) t dt
= - 12 [2t3/2 - 25t5/2 ] + C
= -t3/2 + 15t5/2 + C
x = 2 ⇒ t = 1: f( 2) = -1 + 15 + C = - 45 + C
∵ f( 2) = - 45 ⇒ C = 0
x = 1 ⇒ t = 2: f(1) = -2 2 + 4 25
= - 6 25
Answer: (1)
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