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gtnhenbr [62]
2 years ago
6

Analyzing Graphs of Functions

Mathematics
1 answer:
liberstina [14]2 years ago
6 0

Answer:

The first option

Step-by-step explanation:

If you look at the graph, you'll realize that when x = 2 in the first graph, y = 4

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hoa [83]

Answer:

a) This integral can be evaluated using the basic integration rules. \int 11x^{4}dx = \frac{11}{5} x^{5}+C

b) This integral can be evaluated using the basic integration rules. \int 8x^{1}x^{4}dx=\frac{4}{3}x^{6}+C

c) This integral can be evaluated using the basic integration rules. \int 3x^{31}x^{4}dx=\frac{x^{36}}{12}+C

Step-by-step explanation:

a) \int 11x^{4}dx

In order to solve this problem, we can directly make use of the power rule of integration, which looks like this:

\int kx^{n}=k\frac{x^{n+1}}{n+1}+C

so in this case we would get:

\int 11x^{4}dx=11 \frac{x^{4+1}}{4+1}+C

\int 11x^{4}dx=11 \frac{x^{5}}{5}+C

b) \int 8x^{1}x^{4}dx

In order to solve this problem we just need to use some algebra to simplify it. By using power rules, we get that:

\int 8x^{1}x^{4}dx=\int 8x^{1+4}dx=\int 8x^{5}dx

So we can now use the power rule of integration:

\int 8x^{5}dx=\frac{8}{5+1}x^{5+1}+C

\int 8x^{5}dx=\frac{8}{6}x^{6}+C

\int 8x^{5}dx=\frac{4}{3}x^{6}+C

c) The same applies to this problem:

\int 3x^{31}x^{4}dx=\int 3x^{31+4}dx=\int 3x^{35}dx

and now we can use the power rule of integration:

\int 3x^{35}dx=\frac{3x^{35+1}}{35+1}+C

\int 3x^{35}dx=\frac{3x^{36}}{36}+C

\int 3x^{35}dx=\frac{x^{36}}{12}+C

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3 years ago
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