Integrate $\int\sqrt{1-x^2}dx$

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Final answer to the problem

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

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

Impara online a risolvere i problemi di integrali con radicali passo dopo passo.

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

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Impara online a risolvere i problemi di integrali con radicali passo dopo passo. Integrate int((1-x^2)^(1/2))dx. We can solve the integral \int\sqrt{1-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. Applying the trigonometric identity: 1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2.

Final answer to the problem

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

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

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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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