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Integrate $\int\sqrt{16-x^2}dx$

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Solution

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Final answer to the problem

$2\arcsin\left(\frac{x}{4}\right)+\frac{1}{8}x\sqrt{16-x^2}+C_0$
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We can solve the integral $\int\sqrt{16-x^2}dx$ by applying integration method of trigonometric substitution using the substitution

$x=4\sin\left(\theta \right)$

Learn how to solve integrali con radicali problems step by step online.

$x=4\sin\left(\theta \right)$

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Learn how to solve integrali con radicali problems step by step online. Integrate int((16-x^2)^(1/2))dx. We can solve the integral \int\sqrt{16-x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Factor the polynomial 16-16\sin\left(\theta \right)^2 by it's greatest common factor (GCF): 16.

Final answer to the problem

$2\arcsin\left(\frac{x}{4}\right)+\frac{1}{8}x\sqrt{16-x^2}+C_0$

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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

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Function Plot

Plotting: $2\arcsin\left(\frac{x}{4}\right)+\frac{1}{8}x\sqrt{16-x^2}+C_0$

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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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Main Topic: Integrali con radicali

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