   Chapter 7.8, Problem 3E

Chapter
Section
Textbook Problem

# Find the area under the curve y = 1 / x 3 from x = 1 to x = t and evaluate it for t = 10 , 100, and 1000. Then find the total area under this curve for x ≥ 1 .

To determine

To find:

The area under the given curve, and then evaluate it for t= 10, 100, 1000, then find the total area under the curve for x ≥1.

Explanation

Given:

y=1x3

Formulae used:

The method of integral by direct integration

Consider y=1x3

Use the formulae of integral direct integration.

Now according to the given expression, the value of the area under the curve y=1x3 from x=1 to x=t is

Area=1t1x3dx=[x22]1t=12(1t21)Thus area from x=1 to x=t is, A(t)=1212t2

Thus, put the value of the t=10,100 and 1000 and get:

For t=10

A(t)=1212t2=121200=0

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