# `y = x^(-4), 1<=x<=6` Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

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Expert Answers

gsarora17 | Certified Educator

Refer the graph in the attached image.

From the graph,

Area of the region that lies beneath the curve `~~` 6/100(Area of Rectangle)

Area of the region `~~` 6/100(5*1) `~~` 0.30

Exact Area of the region=`int_1^6x^(-4)dx`

`=[x^(-4+1)/(-4+1)]_1^6`

`=[x^(-3)/-3]_1^6`

`=[-1/(3x^3)]_1^6`

`=-1/3(1/6^3-1/1^3)`

`=-1/3(1-6^3)/(6^3)`

`=-1/3(-215/216)`

`=0.33179`

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