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2 years ago

Can you help me in this question?

Mathematics

1 answer:

gregori [183]2 years ago

3 0

Answer: I think its B

Step-by-step explanation: My friend answered it.

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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

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

Unit: Integration

5 0

1 year ago

X/3-4=-7 please help me solve

Vanyuwa [196]

In order to solve this we need to get x by itself on one side.

We need o start by adding across the 4 so that we get:

x/3 = -7 + 4 = -3

We then need to multiply both sides by 3 to get a singular x:

x = -3 * 3 = -9

5 0

2 years ago

Read 2 more answers

Let (12,-5) be a point on the terminal side of an angle 0. Find the values of sin e, cose, and tan

lord [1]

Answer:

Sin = -5/13

Cos = 12/13

Tan = -5/12

Step-by-step explanation:

5 0

2 years ago

Alexandra invested $610 in an account paying an interest rate of 7 3/8% compounded

shusha [124]

Exact answer: 165.5754

Rounded to the nearest dollar: 166

4 0

2 years ago

Patty is a customer service representative for a company. She earns $18 an hour, plus an additional $2.50 each time one of her c

nlexa [21]

Answer:

C.18(38) +2.5s >/= 750

Step-by-step explanation:

7 0

2 years ago