Calc-Quadrants

[johnny101]

I'm having trouble on this question:
Find the area of the region in the first quadrant that is bounded above by the curve y= sq rt x and below by the x-axis and the line y=x -2.
Does anyone have any steps they can offer or an example like problem?

 

[pka]

I'm having trouble on this question:
Find the area of the region in the first quadrant that is bounded above by the curve y= sq rt x and below by the x-axis and the line y=x -2.
Does anyone have any steps they can offer or an example like problem?

First, PLOT THE GRAPHS.

In the first quadrant you need two different integrals: \(\displaystyle \int_0^2 {f(x)dx} + \int_2^4 {f(x)dx} \).

HINT: on one of those the lower function is \(\displaystyle y=0\) on the other it is \(\displaystyle y=x-2\) .

 

[johnny101]

I understand the graph obviously I guess I'm confused on the integral section of it, isn't it f-g essentially so how would that be with the integrals?

 

[stapel]

I understand the graph obviously

See, that was information that might have been useful to include in your original post; something like, "I've done the graph and can 'see' the region and that I'll need two integrals, but..." Then we'd have known that you'd already done that bit. This is why we ask that students show what they've done so far.

I guess I'm confused on the integral section of it, isn't it f-g essentially so how would that be with the integrals?

What do you mean by "isn't it f-g essentially"? What is the "it"? Are you maybe referring to pairs of functions or other upper and lower bounds of the regions? What do you mean by "how would that be with the integrals"? How would what be? Have you not yet covered integration with a function (rather than the x-axis or other horizontal line) as the lower bound of the graphed region?

Please reply with clarification, starting with the x-values defining the two intervals over which you'll be integrating, and what functions you see as the upper and lower bounds (from the graph) for each. Thank you!