Pleaseeee help I need a answer fast

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

Unit: Integration

5 0

2 years ago

Evaluate x(y+3)/(3+y)z for x=12, y=1, and z=6. A) 2 B) 5 C) 8 D) 6

fgiga [73]

Answer:

2

Step-by-step explanation:

We take the equation

$x(y+3)/(3+y)z$

and substitute the values for each individual variable in the problem. It looks like this:

$12(1+3)/(3+1)6$

Now we can solve the equation.

When solved, it equals 2.

5 0

3 years ago

Read 2 more answers

*HELP PLEASE*

aksik [14]

If two events are disjoint (i.e. mutually exclusive) they cannot both occur and so we can determine probabilties by simple addition:

$P(AorB)=P(A)+P(B)$
$P(AorB)=\frac{40}{61}+\frac{2}{61}$
$P(AorB)=\frac{42}{61}$
$P(AorB)\approx 68.8\%$

A more complete answer would use a joint probability table but that's difficult to type out/format correctly here.

7 0

4 years ago

Answerr please .........................

AlexFokin [52]

Answer: I think its the third choice. It's asking for the progress of the height.

8 0

4 years ago

Read 2 more answers

Did I do this right? If not please explain!

andrew11 [14]

Yep! Good job, you did it correctly.
Your y-intercept is equal to the constant of the equation (y-int = -2). Your movement/direction (or rise over run) is equal to the variable. Since your variable is x (which can also be written as 1x) means you move up one and over one (rise over run). This is because 1/1 is equal to 1.

5 0

3 years ago