SOLUTION: Find the area between the curves for the equations below and round your answer to one decimal place. y = x2 + 4x – 4 and y = x + 3

Algebra ->  Equations -> SOLUTION: Find the area between the curves for the equations below and round your answer to one decimal place. y = x2 + 4x – 4 and y = x + 3       Log On


   

Question 966190: Find the area between the curves for the equations below and round your answer to one decimal place.
y = x2 + 4x – 4 and y = x + 3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area between the curves for the equations below and round your answer to one decimal place.
y = x2 + 4x – 4 and y = x + 3
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Find the 2 intersections
x + 3 = x^2 + 4x - 4
x%5E2+%2B+3x+-+7+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-7=37.

Discriminant d=37 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+37+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+37+%29%29%2F2%5C1+=+1.54138126514911
x%5B2%5D+=+%28-%283%29-sqrt%28+37+%29%29%2F2%5C1+=+-4.54138126514911

Quadratic expression 1x%5E2%2B3x%2B-7 can be factored:
1x%5E2%2B3x%2B-7+=+%28x-1.54138126514911%29%2A%28x--4.54138126514911%29
Again, the answer is: 1.54138126514911, -4.54138126514911. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-7+%29

x = -4.54138
x = 1.54138
The x values are the limits of integration, the y values are not needed.
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f(x) = x^2 + 3x - 7
INT(x) = x%5E3%2F3+%2B+3x%5E2%2F2+-+7x --- Ignore the constant of INT
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Area = INT(1.54139) - INT(-4.54138)
Area =~ 37.5 sq units