Describe different ways that you can show a story problem?

Use integration by parts to find the integrals in Exercise.<br> ∫^3_0 3-x/3e^x dx.

Viefleur [7K]

Answer:

8.733046.

Step-by-step explanation:

We have been given a definite integral $\int _0^3\:3-\frac{x}{3e^x}dx$ . We are asked to find the value of the given integral using integration by parts.

Using sum rule of integrals, we will get:

$\int _0^3\:3dx-\int _0^3\frac{x}{3e^x}dx$

We will use Integration by parts formula to solve our given problem.

$\int\ vdv=uv-\int\ vdu$

Let $u=x$ and $v'=\frac{1}{e^x}$ .

Now, we need to find du and v using these values as shown below:

$\frac{du}{dx}=\frac{d}{dx}(x)$

$\frac{du}{dx}=1$

$du=1dx$

$du=dx$

$v'=\frac{1}{e^x}$

$v=-\frac{1}{e^x}$

Substituting our given values in integration by parts formula, we will get:

$\frac{1}{3}\int _0^3\frac{x}{e^x}dx=\frac{1}{3}(x*(-\frac{1}{e^x})-\int _0^3(-\frac{1}{e^x})dx)$

$\frac{1}{3}\int _0^3\frac{x}{e^x}dx=\frac{1}{3}(-\frac{x}{e^x}- (\frac{1}{e^x}))$

$\int _0^3\:3dx-\int _0^3\frac{x}{3e^x}dx=3x-\frac{1}{3}(-\frac{x}{e^x}- (\frac{1}{e^x}))$

Compute the boundaries:

$3(3)-\frac{1}{3}(-\frac{3}{e^3}- (\frac{1}{e^3}))=9+\frac{4}{3e^3}=9.06638$

$3(0)-\frac{1}{3}(-\frac{0}{e^0}- (\frac{1}{e^0}))=0-(-\frac{1}{3})=\frac{1}{3}$

$9.06638-\frac{1}{3}=8.733046$

Therefore, the value of the given integral would be 8.733046.

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3 years ago

a ballroom is being set up for a banquet in one room there are 7 tables and 56 chairs how many tables should be set up for 40 ch

Jobisdone [24]

Answer:

points

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Mike collected data to determine the amount of traffic on his street throughout the day. Identify the striking deviation in his

Norma-Jean [14]

Answer:

B

Step-by-step explanation:

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3 years ago

Assume that the U.S. PPF measures oil and gas production on the x-axis and production of other goods and services on the y-axi

iris [78.8K]

Answer:

The U.S. PPF rotates outward (abticlockwisely), increasing the x-axis intercept with no change in the y-axis intercept

Step-by-step explanation:

Fracking is a method of improving production capabilities on oil and gas production. Although, it usually leads to environmental pollution later, it does bring in higher yields of oil and gas.

If the oil and gas production on the x-axis increases without a simultaneous, almost equal increase in production of other goods and services (on the y-axis), the data points for the x-axis shift more to the right and the PPF rotates more anti-clockwisely outward, thereby increasing the intercept on the now improved x-axis and not too much change on the intercept of the y-axis.

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3 years ago

using the point-slope formula, what is the equation of the line that passes through the points (1, 5) and (0, 0)? a. y = x b. y

Dmitry_Shevchenko [17]

First we find the slope m as follows:
$m=\frac{y-y_{1}}{x-x_{1}}=\frac{5-0}{1-0}=5$
So the equation is of the form:
y = 5x + b
When x = 1, y = 5. Therefore b = 0.
So the equation is:
y = 5x

4 0

3 years ago