ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the trigonometric integral $\int\sqrt{\sin\left(x\right)}\cos\left(x\right)dx$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

###  Videos

$\frac{2}{3}\sqrt{\sin\left(x\right)^{3}}+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

We can solve the integral $\int\sqrt{\sin\left(x\right)}\cos\left(x\right)dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $\sin\left(x\right)$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

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

Learn how to solve discriminant of quadratic equation problems step by step online.

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

Learn how to solve discriminant of quadratic equation problems step by step online. Solve the trigonometric integral int(sin(x)^1/2cos(x))dx. We can solve the integral \int\sqrt{\sin\left(x\right)}\cos\left(x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sin\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

$\frac{2}{3}\sqrt{\sin\left(x\right)^{3}}+C_0$

##  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 sinx^0.5cosxdx using basic integralsSolve integral of sinx^0.5cosxdx using u-substitutionSolve integral of sinx^0.5cosxdx using integration by partsSolve integral of sinx^0.5cosxdx using weierstrass substitution

SnapXam A2

Go!
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

### Main Topic: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.