25. The graph of f(x) is given. For the following questions, F'(x) = f (x). f(x) -Area=8 7. 10 6. Area=5 (a) If F(-3) = 2, find F(1). Solution: f(x) dx = 2 – 5 = -3. F(1) = F(-3) + f (x) -3 (b) Using above information, find F(5). Solution: f (x) dx = F(5) = F(1) + -3+8 = 5. || 2-
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
How did they find the solution? I am confused where the numbers are coming from.
Since f(x) is derivative of F(x). So F(x) is antiderivative of f(x).
a) You have to find F(1) , given F(-3)=2
So, we try to find a relation between F(-3) and F(1).
From the graph we have an area between -3 to 1. We try to use that.
Area under f(x) between -3 to 1 is given by:
Simplify the integral.
![Lf(x)dx
J-3
=[F(x)]!3
=F(1)-F(-3)](https://content.bartleby.com/qna-images/answer/542fd813-1875-4e78-aba2-193ffc987e5b/a9ff463d-86cb-4dd6-bc08-0dcf3bd4ce49/9hquoee.png)
From the integral we get the relation which they have used.
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