area bounded by a curve??

[scatteam_2]

The area bounded by the curve y= 1/3-x, the x axis, the y axis and the line x=2 is..........................??

[qshyrn]

The area bounded by the curve y= 1/3-x, the x axis, the y axis and the line x=2 is..........................??

integrate  1/3-x from 0 to 2

[brightsky]

First find:

Substitute

So

Subbing back in: .

So for the indefinite integral from x = 0 to x = 2, we want:

[m@tty]

Alternatively, since substitution is actually not on the methods syllabus and hence it is not taught to the majority, when anti-differentiating write it in a form such that the numerator is the derivative of the denominator. Then simply recognise that as anti-differentiating to a natural logarithm.

Anyway, .