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3 years ago

Uh not sure if i put it in the right subject but... help Imao

Mathematics

1 answer:

kondaur [170]3 years ago

4 0

Answer:

yes u did put in right subject

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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

-1/3 + (-7/4)<br><br> Ill give this cookie to who solves it

elena-14-01-66 [18.8K]

Answer:

-25/12

Step-by-step explanation:

first, you need a common denominator. in this case, it's 12.

-1/3=-4/12

-7/4=-21/12

and then you add

-4+-21=-25

so -25/12 is your answer

5 0

2 years ago

Read 2 more answers

I need help solving a system of linear equation, and it says to solve it by Substitution.

olga_2 [115]

2x - 3y = -24
x+ 6y = 18

you solve the first one by the x:

2x = -24 + 3y

x = (-24+3y)/2

then you substitute what you found in the other equation and you solve by y

(-24+3y)/2 + 6y = 18 multiply everything by 2

-24 + 3y + 12y = 36

3y + 12y = 36 + 24

15y = 60

y = 60/15

y = 4

Good job! You found your y! :D

Now let's substitute the y in the first equation with 4:

2x - 3(4) = -24

2x - 12 = -24

2x = -24 + 12

2x = -12

x = -12/2

x= -6

Done!! ;) <span />

6 0

2 years ago

Read 2 more answers

Jessica made 8 out of 24 free throws. Bob made 5 out of 20 free throws. Who has the highest free throw ratio ?

Gnoma [55]

8 out of 24 = 1 out of 3

5 out of 20 = 1 out of 4

1/3 is larger that 1/4
Jessica has the largest ratio

6 0

1 year ago

Find the product or quotient for each. simple form<br> 5/9 divide 5/6

MakcuM [25]

Answer: 2/3

Step-by-step explanation:

5/9 and 5/6 doesn't have the same denominator. So 5/9 changes to 10/18, while 5/6 changes to 15/18.

10/18 divided by 15/18= 10/18 x 18/15 = 180/270

180/270= 2/3

8 0

2 years ago