# How do you find the area between #f(x)=x^2+2x+1# and #g(x)=2x+5#?

The area is

Start by finding the intersection points.

Substitute the second equation into the first.

The solution set is hence

So, our goal is to subtract the area of the lower graph,

We do this by integrating.

Let's start with finding the area of the upper graph.

Now for the lower graph.

Subtract:

Hence, the area between

Hopefully this helps!

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To find the area between the curves ( f(x) = x^2 + 2x + 1 ) and ( g(x) = 2x + 5 ), you need to first determine the points where the two curves intersect by setting them equal to each other and solving for ( x ). Then integrate the absolute difference of the two functions over the interval of intersection from the smaller x-coordinate to the larger x-coordinate. The integral expression for the area would be:

[ \int_{x_1}^{x_2} |f(x) - g(x)| , dx ]

where ( x_1 ) and ( x_2 ) are the x-coordinates of the points of intersection. After finding the intersection points, integrate ( |f(x) - g(x)| ) with respect to ( x ) over the interval from ( x_1 ) to ( x_2 ). The resulting value will be the area between the curves.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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