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Integrate the function $\sqrt{16-4x^2}$ from $-2$ to $2$

Step-by-step Solution

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Solution

Final answer to the problem

$4\pi $
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Step-by-step Solution

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1

Primeiro, fatoramos os termos dentro do radical por $4$ para reescrever os termos de uma forma mais conveniente

$\int_{-2}^{2}\sqrt{4\left(4-x^2\right)}dx$

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$\int_{-2}^{2}\sqrt{4\left(4-x^2\right)}dx$

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Learn how to solve problems step by step online. Integrate the function (16-4x^2)^1/2 from -2 to 2. Primeiro, fatoramos os termos dentro do radical por 4 para reescrever os termos de uma forma mais conveniente. Tiramos a constante do radical. Podemos resolver a integral \int2\sqrt{4-x^2}dx usando o método de integração de substituição trigonométrica. Tomamos a mudança de variável. Agora, para reescrever d\theta em termos de dx, precisamos encontrar a derivada de x. Portanto, precisamos calcular dx, podemos fazer isso derivando a equação da etapa anterior.

Final answer to the problem

$4\pi $

Exact Numeric Answer

$12.566371$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of ((16+-4x^2)^0.5)dx from -2 to 2 using partial fractionsSolve integral of ((16+-4x^2)^0.5)dx from -2 to 2 using basic integralsSolve integral of ((16+-4x^2)^0.5)dx from -2 to 2 using u-substitutionSolve integral of ((16+-4x^2)^0.5)dx from -2 to 2 using integration by partsIntegrate using trigonometric identitiesSolve integral of ((16+-4x^2)^0.5)dx from -2 to 2 using trigonometric substitution

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Function Plot

Plotting: $\sqrt{16-4x^2}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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