Find the area of the region bounded by y=1/x^2, y=4, and x=5. Use any method/

81/5

Step-by-step explanation:

See image.

I always think drawing these out helps.

I had to find lower limit for x by finding when 1/x^2=4

x^2=1/4

This implies x=1/2 since in the picture x is positive.

We need to evaluate

Integral( 4 - 1/x^2 , from x=1/2 to x=5)

Or

Integral( 4 - x^-2 , from x=1/2 to x=5)

=4x+x^-1 ] from x=1/2 to x=5

(4×5+5^-1)-(4×1/2+(1/2)^-1)

(20+1/5)-(2+2)

20-(2+2)+1/5

20-4+1/5

16+1/5

81/5