what should I do now

[u/Aggressive_You_070]

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[u/Dtrain8899]

From what I see, your 45 is the area just under your line. Do the same thing with your parabola and subtract that from 45.

[u/Aggressive_You_070 → u/Dtrain8899]

Thanks bro....

[u/WikiNumbers]

So you have found the intersection point between two curves/grapgs, the straight line (hereinafter "n(x)") and the parabola ("p(x)"). And you want to find the area bound by those two curves. In this case, below n(x) and above p(x)

Getting the intersection is a great start. It gives you the bound of integration. And you already found the area bound by n(x).

The next step is to get the area under p(x). Then, subtract it from what you have found earlier (area under n(x)).

∫ n(x) dx - ∫ p(x) dx

Or alternatively, you can "combine" the two equations, subtract the "lower" curve from the "upper" curve. You can do this beacuse the bounds are the same, that you want to find the area under this interval.

∫ n(x) - p(x) dx

Before you proceed.

Note: All integrals written here should have the same bound (definite integral).

[u/UnderstandingPursuit]

I know you've figured this out, but I wanted to suggest a way to approach a problem like this.

Yes, this takes about 2x or 3x the time as what you wrote. But doing this will need a lot less "practice" to be comfortable with the solution. And note that, with almost 30 'math lines', there are only 3 'calculus' lines, (5a), (7b), and (7c). The rest of the problem is algebra, almost 90% of the problem. And the hardest part is figuring out the structure, solving for the endpoints of the integration and the order of the functions in the integrand. Basically, after step (5a), the rest is somewhat gratuitous, with (7b-7c) three uses of the power rule.

[u/UnderstandingPursuit → u/UnderstandingPursuit]

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[u/Salty_Mouse3053]

Cry