Okay looking at the diagram below, notice the red line. It is the shape of a
trapezium.You can find the area under the
curve and from this value MINUS the area under the
line.
First I found the two points at which the curve and line intersect :
x
2 - 4x +4 = 7-2x
Hence, x
2-2x -3 =0
Solving for x gives : 3 and -1
Inputting the above x values into 7-2x = y give corresponding y coordinates of : 1 and 9
Finding the area under the line :
![\frac{1}{2}(1+9)*4=20](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{1}{2}(1+9)*4=20)
Next I integrate the curve to get :
![\frac{(x-2)^3}{3}](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{(x-2)^3}{3})
Inputting 3 into above gives a value of 1/3 .
Inputting -1 into abov gives : -9
Hence 1/3 - - 9 =
![\frac{28}{3}](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{28}{3})
Hence, 20 -
![\frac{28}{3}](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{28}{3})
=
![10 \frac{2}{3}](https://studentforums.biz/cgi-bin/mimetex.cgi?10 \frac{2}{3})