Question

The odd natural number a, such that the area of the region bounded by $y = 1, y = 3, x = 0, x = y^a$ is $\frac {364}{3}$, is equal to

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

Answer: (B)

5

Answer 2

$|∫_1^3y^ady|=\frac {364}{3}$

$|\frac {1}{a+1}(y^{a+1})|_1^3=\frac {364}{3}$

$\frac {3a+1−1}{a+1}=±\frac {364}{3}$
Solving with (+) sign,
$\frac {3a+1−1}{a+1}=\frac {364}{3}$
$a=5$
Solving with (-) sign,
$\frac {3a+1−1}{a+1}=-\frac {364}{3}$
No a exist
$∴a=5$

So, the correct option is (B): $5$