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Q.

Area enclosed by the curve given by $| x − 60 | + | y | = x 4$

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answer is 480.

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Detailed Solution

$c a s e (i) x < 0 | y | = − x 4 + x − 60 = 3 x 4 − 60$
LHS= -ve not possible
$Case (ii) Let 0 ≤ x ≤ 60$
$| y | = ∣ x 4 + x − 60 = 5 x 4 − 60 ≥ 0 ⇒ x ≥ 48 Case (i i i) x ≥ 60 | y | = x 4 − (x − 60) = − 3 x 4 + 60 ⇒ 60 − 3 x 4 ≥ 0 ⇒ x ∈ [60, 80]$
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$∴$ Required area 480

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Area enclosed by the curve given by |x−60|+|y|= x 4