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3 years ago

Help with proofs please

Mathematics

1 answer:

nirvana33 [79]3 years ago

5 0

Answer:

B. Division Property of Equality

Step-by-step explanation:

Hope it helps.

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Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to find the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

5 0

2 years ago

PLEASE HELP, question in image

Mashcka [7]

You have the right answer but for the second part it's 65+10/5=x

4 0

3 years ago

Read 2 more answers

Pls help this is for math ill give a brainly

olasank [31]

Answer: The last one - 5 1/3 divided by 1/6

Step-by-step explanation:

since you are trying to figure out how much she runs a day, u divide

Hope this helps :)

6 0

3 years ago

22. Solve the system

DaniilM [7]

Equation 1) x + 6y = 2
Equation 2) 5x + 4y = 36

Multiply all of equation 1 by 5.

1) 5(x + 6y = 2)

Simplify.

1) 5x + 30y = 10
2) 5x + 4y = 36

Subtract equations from one another.

26y = -26

Divide both sides by 26.

y = -1

Plug in -1 for y in the first equation.

x + 6y = 2

x + 6(-1) = 2

Simplify.

x - 6 = 2

Add 6 to both sides.

x = 8

D : (8, -1)

~Hope I helped!~

8 0

3 years ago

Please help show work please

Lubov Fominskaja [6]

Answer:

Step-by-step explanation

it hard to explain

7 0

3 years ago

Read 2 more answers