1 point find the area of the region enclosed between...

Find the area of the region enclosed between f(x) = x^2 + 3x + 19 and g(x) = 2x^2 + 0x + 1. Area = (Note: The graph above represents both functions f and g but is intentionally left unlabeled.)

Transcript

00:01 Hello, according to the given graph, so here we have fx and as well as we have a given that is f of x is equal to x square plus 3x plus 19.

00:13 And from the given graph that is fx is a blue curve.

00:16 So, this is f of x and the red curve that is g of x.

00:23 Now, here we have a given that is f of x.

00:25 So, this can be written as that is 3x.

00:29 So, expanding the term from here we have f of x is equal to x plus 3 divided by 2 whole square plus 67 divided by 4.

00:41 Now, from here x plus 3 divided by 2 whole square is positive that is greater than equal to 0.

00:48 So, also adding for both side by 67 by 4.

00:52 So, we have x plus 3 divided by 2 whole square plus 67 divided by 4 is less than equal to greater than equal to 67 divided by 4.

01:04 So, we have f of x that is greater than equal to 67 divided by 4.

01:10 Now, we can say that is red curve is not of f of x.

01:14 So, red curve has a value that are the negative.

01:16 So, we have the f of x is blue curve and g of x is red curve.

01:20 For point of intersection of the limit integration.

01:23 So, we have f of x is equal to g of x.

01:28 So, it is given that is g of x in the question that is 2x square plus 2x minus 1.

01:35 So, putting the value from here we can write it as x square plus 3x plus 90 is equal to 2x square plus 2x minus 1.

01:46 Now, solving further from here we can get it as that is x square minus x minus 20 is equal to 0...

Question

Find the area of the region enclosed between f(x) = x^2 + 3x + 19 and g(x) = 2x^2 + 0x + 1. Area = (Note: The graph above represents both functions f and g but is intentionally left unlabeled.)

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