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A farmer {F}_{{1}}has a land in the shape of a triangle with v

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A farmer $F_{1}$ has a land in the shape of a triangle with vertices at $P (0, 0), Q (1, 1)$ and $R (2, 0)$ . From this land, a neighbouring farmer $F_{2}$ takes away the region which lies between the side $P Q$ and a curve of the form $y = x^{n} (n > 1)$ . If the area of the region taken away by the farmer $F_{2}$ is exactly 30% of the area of $P Q R$ , then the value of $n$ is _______.

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A farmer

F_{1}

has a land in the shape of a triangle with vertices at

P (0, 0), Q (1, 1)

and

R (2, 0)

. From this land, a neighbouring farmer

F_{2}

takes away the region which lies between the side

P Q

and a curve of the form

y = x^{n} (n > 1)

. If the area of the region taken away by the farmer

F_{2}

is exactly 30% of the area of

P Q R

, then the value of

n

is _______.

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Question Text	A farmer $F_{1}$ has a land in the shape of a triangle with vertices at $P (0, 0), Q (1, 1)$ and $R (2, 0)$ . From this land, a neighbouring farmer $F_{2}$ takes away the region which lies between the side $P Q$ and a curve of the form $y = x^{n} (n > 1)$ . If the area of the region taken away by the farmer $F_{2}$ is exactly 30% of the area of $P Q R$ , then the value of $n$ is _______.
Answer Type	Video solution: 1
Upvotes	150