First slide

Area of bounded Regions

Question

$The area of the region bounded by the two curves y = \sqrt{1 - x^{2}}$ $and y = (| x | - 1)^{4} is (\frac{π}{2} - λ) square units, then λ = \frac{p}{q}, where p, q are coprime$ $natural numbers. Then p^{q} + q^{p} =$

Difficult

Solution

$A r e a o f t h e r e g i o n b o u n d e d b y t h e c u r v e s = 2 (\frac{π}{4} - \int_{0}^{1} {(x - 1)}^{4} d x) = \frac{π}{2} - 2 (\frac{1}{5})$
$p = 2, q = 5 \Rightarrow p^{q} + q^{p} = 32 + 25 = 57$

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