Question

The graph of f is shown in the figure to the right. Let \begin{align*} A(x) = \int_{-2}^{x} f(t) \, dt \quad \text{and} \quad F(x) = \int_{4}^{x} f(t) \, dt \end{align*}be two area functions for f. Evaluate the following area functions. a. A(-2) b. F(8) c. A(4) d. F(4) e. A(8)

          The graph of f is shown in the
figure to the right. Let
\begin{align*}
A(x) = \int_{-2}^{x} f(t) \, dt \quad \text{and} \quad F(x) = \int_{4}^{x} f(t) \, dt
\end{align*}be two area functions for f.
Evaluate the following area
functions.
a. A(-2) 		b. F(8) 		c. A(4)
d. F(4) 		e. A(8)
        
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The graph of f is shown in the
figure to the right. Let

    A(x) = ∫-2^x f(t)   dt   and   F(x) = ∫4^x f(t)   dt
be two area functions for f.
Evaluate the following area
functions.
a. A(-2) 		b. F(8) 		c. A(4)
d. F(4) 		e. A(8)

Added by Mackenzie D.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Solve for a, b, c, d, e. The graph of f is shown in the figure to the right. Let X be the x-axis and y be the y-axis. Area = 16. Let A(x) = ∫f(x)dx and F(x) = ∫(a√(Area - 2))dx be two area functions for f. Evaluate the following area functions: a. A-2 b. F8 c. A4 d. F4 e. A8
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The graph of f is shown in the figure to the right. Let A(x)=∫_{-2}^x f(t) dt and F(x)=∫_4^x f(t) dt be two area functions for f. Evaluate the following area functions. a. A(-2) b. F(8) c. A(4) d. F(4) e. A(8)

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Transcript

-
00:01 In this question we are given the graph of f and we define a of x to be the integral of f of t from negative two to x and the f of x is the integral from 4 to x f of t d t so in part a we are asked a of negative 2 it is the integral from the integral from 4 to x f of t d t so in part a we are asked the a of negative 2.
00:33 It is as an integral from negative 2 to negative 2, so the answer should be 0.
00:49 Part b is f of 8, so it is integral from 4 to 8, f of t d t.
00:59 So from 4 to 8, the area is 8, but it is below the horizontal axis, so it is negative 8.
01:22 Next we go on to part c...
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