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# Integrate the function $\cos\left(x\right)^2$ from $1$ to $3$

## Step-by-step Solution

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###  Videos

$0.702822$
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## Step-by-step Solution

Problem to solve:

$\int_{1}^{3}\cos\left(x\right)^2dx$

Specify the solving method

1

Rewrite the trigonometric expression $\cos\left(x\right)^2$ inside the integral

$\int_{1}^{3}\frac{1+\cos\left(2x\right)}{2}dx$
2

Take the constant $\frac{1}{2}$ out of the integral

$\frac{1}{2}\int_{1}^{3}\left(1+\cos\left(2x\right)\right)dx$

Learn how to solve definite integrals problems step by step online.

$\int_{1}^{3}\frac{1+\cos\left(2x\right)}{2}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function cos(x)^2 from 1 to 3. Rewrite the trigonometric expression \cos\left(x\right)^2 inside the integral. Take the constant \frac{1}{2} out of the integral. Expand the integral \int\left(1+\cos\left(2x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral of a constant is equal to the constant times the integral's variable.

$0.702822$

##  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 int(cos(x)^2)dx&1&3 using basic integralsSolve int(cos(x)^2)dx&1&3 using u-substitutionSolve int(cos(x)^2)dx&1&3 using integration by partsSolve int(cos(x)^2)dx&1&3 using tabular integrationSolve int(cos(x)^2)dx&1&3 using weierstrass substitution
SnapXam A2

### beta Got a different answer? Verify it!

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

$\int_{1}^{3}\cos\left(x\right)^2dx$

### Main topic:

Definite Integrals

~ 0.09 s