1. Definite Integration

The question on my paper has a graph, with the curve $x^2 - 6x + 11$ and the line $-x + 7$

It asks to find the co-ordinates of the points $A$ and $B$

and for the area of the shaded region bounded by the curve and under the line.

$A (1 , 6) B (4 , 3)$

and for the area, I had $11\frac{1}{2} units^2$

Could someone please check if this is right?

2. Originally Posted by db5vry
The question on my paper has a graph, with the curve $x^2 - 6x + 11$ and the line $-x + 7$

It asks to find the co-ordinates of the points $A$ and $B$

and for the area of the shaded region bounded by the curve and under the line.

$A (1 , 6) B (4 , 3)$

and for the area, I had $11\frac{1}{2} units^2$

Could someone please check if this is right?
The intersection points are correct. How did you get the area answer?

3. Originally Posted by danny arrigo
The intersection points are correct. How did you get the area answer?
I integrated the value of the curve and the value of the line
And then inserted the values of the x-co-ordinates (4 and 1) and took the answers away from each other
for the curve I had 25 units squared
for the line I had 13 and a half units squared
I took one away from the other to get 11 and a half units squared.
Is this right?

4. Originally Posted by db5vry
I integrated the value of the curve and the value of the line
And then inserted the values of the x-co-ordinates (4 and 1) and took the answers away from each other
for the curve I had 25 units squared
for the line I had 13 and a half units squared
I took one away from the other to get 11 and a half units squared.
Is this right?
I got different answers. Can you show some detail on the integrations?

5. Originally Posted by danny arrigo
I got different answers. Can you show some detail on the integrations?
It was too much to type so I wrote it out here instead: