Q. 175.0( 1 Vote )

# Evaluate: <span l

dx

- x = x( - 1) = x (x – 1) (x + 1)

- x > 0 for -1 < x < 0

- x < 0 for 0 < x < 1

- x > 0 for 1 < x < 2

NOTE: Sign is only being considered for the range -1≤ x ≤ 2

dx + dx + dx

dx – dx + dx

I = - +

I =

I =

The required value is .

OR

Let, I = …(1)

Using the property of definite Integral: =

I =

I = …(2)

Adding equation 1 and 2 we get –

2I =

2I =

Putting Cos x = t

-Sin x dx = dt

When x = 0 t = 1

x = t = -1

2I = { }

2I = π

2I = π{tan-1(1) – tan-1(-1)} { tan-1(1) = π/4}

2I = π(π/4 – (-π/4))

I =

Hence,

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