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# Integrate the function $\cos\left(\pi x\right)$ from 0 to $1$

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sin
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asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

##  Final answer to the problem

$\frac{1}{\pi }\sin\left(\pi \cdot 1\right)- \left(\frac{1}{\pi }\right)\sin\left(\pi \cdot 0\right)$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Apply the formula: $\int\cos\left(ax\right)dx$$=\frac{1}{a}\sin\left(ax\right)+C$, where $a=\pi$

$\left[\frac{1}{\pi }\sin\left(\pi x\right)\right]_{0}^{1}$
2

Evaluate the definite integral

$\frac{1}{\pi }\sin\left(\pi \cdot 1\right)- \left(\frac{1}{\pi }\right)\sin\left(\pi \cdot 0\right)$

##  Final answer to the problem

$\frac{1}{\pi }\sin\left(\pi \cdot 1\right)- \left(\frac{1}{\pi }\right)\sin\left(\pi \cdot 0\right)$

##  Exact Numeric Answer

$0$

##  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

SnapXam A2

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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: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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