Year 12s: what will be the first way you research your future options? >>

Core 3

I have inegrated and applied the limits 1.5 and 0 to get -10.125 as the area under the curve. But, I'm unsure on how to find the area of the shaded region?

20171117_181120.jpg469.4KB

Reply 1

RDKGames

Study Forum Helper

Original post by Chelsea12345

I have inegrated and applied the limits 1.5 and 0 to get -10.125 as the area under the curve. But, I'm unsure on how to find the area of the shaded region?

You found it, just make it positive since area cannot be negative by definition. You found it negative because the curve is negative in your region of integration.

Reply 2

Chelsea12345

Original post by RDKGames

You found it, just make it positive since area cannot be negative by definition. You found it negative because the curve is negative in your region of integration.

You're right, i just checked the answers page. But,surely the area when integrated is the area under the curve instead of above the curve?

Reply 3

Amullai

Integrating makes makes the area negative for area underneath the line y=0. Just do what RDKGames said and make it positive. This is a really annoying problem when you try to intergrate circles at the origin(obviously i do it for fun because i would have the radius and why bother doing simple stuff)

Reply 4

RDKGames

Study Forum Helper

Original post by Chelsea12345

You're right, i just checked the answers page. But,surely the area when integrated is the area under the curve instead of above the curve?

This is where I dislike the notion of people saying that integration finds the area "below the curve"

In fact, integration finds the area between the curve and the x-axis. The above statement is true if your curve is above the x-axis, as then the area between the curve and the x-axis is in fact below the curve.

Besides, surely the area below the curve in your region of integration would be infinite?