Question
Asked Jun 20, 2019
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Find the area of the following region, expressing your result in terms of the positive integer n 2 2.
1 /n
= x and g(x) =x
The region bounded by f(x)
for x 2 0.
The area of the region in terms of n is
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Find the area of the following region, expressing your result in terms of the positive integer n 2 2. 1 /n = x and g(x) =x The region bounded by f(x) for x 2 0. The area of the region in terms of n is

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Expert Answer

Step 1

Obtain the limits of the integral by equating the functions as follows.

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f(x) g(x) 1 х%3D х" 7 х" %3D| x" х" — х х" — х 3D0 x(x1-1)0 х 3D0 or x* -1-D0 х3D0 or x* -1 (nz 2) х 3D0 or x%3D1

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Step 2

The area of the region bounded by the curves f(x) = x and g(x) = x1/n for x ≥ 0 and n ≥ 2 is given by

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g(x)2(x) 4-(8()-(x)ds A i.e. r" 2 xfor xe (0,1) te

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Step 3

Thus, the integra...

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1 А - х" — х |dх x 1 2 +1 n+1 n+1 (1) (0) (0) 2 п+1 n1 2 2 n п 1 0 2 n+1 n n n1 2

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