Find the area under the curve y = 1/(7x^3) from x = 1 to x = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for x is greater than or equal to 1.

Question

ash2326 · Answer

Let's plot the function first
$$y=\frac 1 {7x^3}$$
for $x\to 0, y\to ?$

anonymous · Answer

ok

ash2326 · Answer

what's the value of y, if x approaches to 0

anonymous · Answer

1/0 so undefined?

anonymous · Answer

i think intergration will Do it..)

ash2326 · Answer

yes $y\to \infty$
now when $x\to \infty$
what value will y approach

anonymous · Answer

I do not know I need help lol

anonymous · Answer

wait y should be undefined not infinity?

ash2326 · Answer

when $x\to \infty$
$$y=\frac 1 \infty=0$$
so the func|dw:1348554320027:dw|tion for x>1 will look like this

ash2326 · Answer

yeah it's undefined, because it approaches infinity

anonymous · Answer

I understand so far

ash2326 · Answer

now let' find the graph. Let's mark x=1 and x=t on the function, t>1 
|dw:1348554417940:dw|