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

Step-by-step Solution

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Solution

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Final Answer

$0.702822$
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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.

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

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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.

Final Answer

$0.702822$

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
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a
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x
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(◻)
+
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

How to improve your answer:

Similar Problems Solved

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Evaluate the integral

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

Main topic:

Definite Integrals

Used formulas:

5. See formulas

Time to solve it:

~ 0.09 s

Related topics:

Definite IntegralsIntegral CalculusCalculusIntegrals of Polynomial FunctionsIntegration by SubstitutionIntegration Techniques

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