$\int_{0}^{r}\frac{r}{\sqrt{r^2-x^2}}dx$

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Final answer to the problem

$r\arcsin\left(\frac{r}{r}\right)-r\arcsin\left(\frac{0}{r}\right)$
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Step-by-step Solution

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Apply the formula: $\int\frac{n}{a}dx$$=n\int\frac{1}{a}dx$, where $a=\sqrt{r^2-x^2}$ and $n=r$

$r\int_{0}^{r}\frac{1}{\sqrt{r^2-x^2}}dx$

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$r\int_{0}^{r}\frac{1}{\sqrt{r^2-x^2}}dx$

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Impara online a risolvere i problemi di integrali definiti passo dopo passo. int(r/((r^2-x^2)^(1/2)))dx&0&r. Apply the formula: \int\frac{n}{a}dx=n\int\frac{1}{a}dx, where a=\sqrt{r^2-x^2} and n=r. Apply the formula: \int\frac{n}{\sqrt{a-b^2}}dx=n\arcsin\left(\frac{b}{\sqrt{a}}\right)+C, where a=r^2, b=x and n=1. Apply the formula: \left(x^a\right)^b=x, where a=2, b=1, x^a^b=\sqrt{r^2}, x=r and x^a=r^2. Apply the formula: \left[x\right]_{a}^{b}=eval\left(x,b\right)-eval\left(x,a\right)+C, where a=0, b=r and x=r\arcsin\left(\frac{x}{r}\right).

Final answer to the problem

$r\arcsin\left(\frac{r}{r}\right)-r\arcsin\left(\frac{0}{r}\right)$

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Function Plot

Plotting: $\frac{r}{\sqrt{r^2-x^2}}$

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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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