The integral -1 32 ( | 2 x ( x) | )dx is equal to:
(3) 1 + 3
Sign of x ( x): it is 0 on [-1, 1] and < 0 on (1, 32 ].
I = -11 2 x ( x) dx - 13/2 2 x ( x) dx
By parts, 2 x ( x) dx = F(x) = ( x) - x ( x)
F(0) = 0, F(1) = , F ( 32 ) = -1
x ( x) is even -11 = 2[F(1) - F(0)] = 2
13/2 = F ( 32 ) - F(1) = -1 -
I = 2 - (-1 - ) = 1 + 3
Answer: (3)
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