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3 years ago

C=pi/2. give your answer in terms of pi. I don't get it. what's the answer??

1 answer:

8 0

Giving your answer in terms of pi means that you dont need to multiply the other number by pi you leave the pi as the answer.
for example : 4pi < --- that is not the answer I am just showing you

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Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

2 years ago

Whats the smallest natural number that has exactly 6 factors and isn't divisible by 2,3 or both

VMariaS [17]

Answer:

- 25

Step-by-step explanation:

5 0

3 years ago

a traffic light is red for 25 sec, yellow for 5 sec, and green for 55 sec. what is the probability that when you reach the light

skad [1K]

I guess the answer 1/5

7 0

3 years ago

Read 2 more answers

Maria studied the traffic trends in India. She found that the number of cars on the road increases by 10% each year. If there we

lord [1]

Answer:

b. 8,800,000.

Step-by-step explanation:

In maria study the number of cars on the road increases by 10% each year.

Total number of cars in the first year =80 million cars.

We will add 10% of 80 million to 80 milion to enable us get the number of cars for the second year.

For year 2 we have;

10% of 80,000,000+80,000,000

$\frac{10}{100}*80,000,000+80,000,000$

8,000,000 + 80,000,000

88,000,000

number of cars in year 2 = 88 million

We will add 10% of 88 million to 88 milion to enable us get the number of cars for the third year.

$\frac{10}{100}*88,000,000+88,000,000$

8,800,000+88,000,000

96,800,000

the number of cars on the road in year 3 compared to year 2 will just be the increase which is in BOLD. That is 8,800,000

<em>or simply subtract the number of cars in year 2 from that in year 3;</em>

96,800,000-88,000,000 = 8,800,000

8 0

3 years ago

Read 2 more answers

Find the distance the point p(0,0,−4)p(0,0,−4) is to the line through the two points q(−4,1,−2q(−4,1,−2 ), and r(−2,0,−5r(−2,0,−

Crazy boy [7]

R(2,0-5r) is the correct answer !!!!!

6 0

3 years ago