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4 years ago

How to evaluate the integral?

Mathematics

1 answer:

DochEvi [55]4 years ago

8 0

Answer:

Step-by-step explanation:

Start from the inside and work outwards, treating any other variables as constant.

$\int\limits^1_{-1} {\int\limits^4_{-4} {(x^2-y^2)} dy\ dx = \int\limits^1_{-1} {(x^2y - y^3/3)^4_1} \, dx = \int\limits^1_{-1} {(3x^2-21)} \, dx$

Can you finish it from here?

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Hector ' s age is 4 less than a number x. Hector is 12 years old. Find the number.

In-s [12.5K]

12+4 =x so you would add 12=4 to get 16. or x=16

3 0

3 years ago

PLEASE HELP ASAP <br>are f(x)=4/x-2-1 and g(x)=3/x+2-2 inverses of each other?

GREYUIT [131]

Answer:

To find the inverse of:

$f (x)=\dfrac{4}{x-2}-1$

Set the function to y:

$\implies y=\dfrac{4}{x-2}-1$

Rearrange to make x the subject:

$\implies y+1=\dfrac{4}{x-2}$

$\implies (y+1)(x-2)=4$

$\implies xy-2y+x-2=4$

$\implies xy+x=2y+6$

$\implies x(y+1)=2y+6$

$\implies x=\dfrac{2y+6}{y+1}$

Swap x and y:

$\implies y=\dfrac{2x+6}{x+1}$

Change y to the inverse of the function sign:

$\implies f$ $\:^{-1}(x)=\dfrac{2x+6}{x+1}$

Rewrite g(x) as a fraction:

$g(x)=\dfrac{3}{x+2}-2$

$\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}$

$\implies g(x)=\dfrac{3-2(x+2)}{x+2}$

$\implies g(x)=\dfrac{3-2x-4}{x+2}$

$\implies g(x)=-\dfrac{2x+1}{x+2}$

Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other

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2 years ago

8+(-3) full work thx If u can help

Kisachek [45]

Answer: 5

Step-by-step explanation:

8+(-3)

=8-3 ⇔ you don't need to change signs when it is positive(+) outside the parenthesis

=5 ⇔ subtraction

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4 years ago

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Alex787 [66]

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4 years ago

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How do you use the distributive property to solve for x in the equation -2(x + 5) = 4

lubasha [3.4K]

Answer:

x = - 7

Step-by-step explanation:

Given

- 2(x + 5) = 4 ← distribute the parenthesis by - 2

- 2x - 10 = 4 ( add 10 to both sides )

- 2x = 14 ( divide both sides by - 2 )

x = - 7

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4 years ago