Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

\int x\cdot \frac{x^2}{\sqrt{16-x^2}}dx

Integral of x(x^2)/((16-1x^2)^0.5)

Answer

$16\int\frac{\sin\left(\theta\right)^{3}\cdot\frac{d}{d\theta}\left(4\sin\left(\theta\right)\right)}{\cos\left(\theta\right)}d\theta$

Step-by-step explanation

Problem

$\int x\cdot \frac{x^2}{\sqrt{16-x^2}}dx$
1

Solve the integral $\int x\frac{x^2}{\sqrt{16-x^2}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=4\sin\left(\theta\right) \\ dx=\frac{d}{d\theta}\left(4\sin\left(\theta\right)\right)d\theta\end{matrix}$

Unlock this step-by-step solution!

Answer

$16\int\frac{\sin\left(\theta\right)^{3}\cdot\frac{d}{d\theta}\left(4\sin\left(\theta\right)\right)}{\cos\left(\theta\right)}d\theta$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

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

Main topic:

Integration by trigonometric substitution

Used formulas:

1. See formulas

Time to solve it:

1.47 seconds