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# Integrate the function $\cos\left(\frac{\pi }{2}x\right)$ from 0 to $1$

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asin
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sinh
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asinh
acosh
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##  Final answer to the problem

$\frac{2}{\pi}$
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##  Step-by-step Solution 

How should I solve this problem?

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

Simplifying

$\int_{0}^{1}\cos\left(\frac{\pi}{2}x\right)dx$

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

$\int_{0}^{1}\cos\left(\frac{\pi}{2}x\right)dx$

Learn how to solve definite integrals problems step by step online. Integrate the function cos(pi/2x) from 0 to 1. Simplifying. Apply the formula: \int\cos\left(ax\right)dx=\frac{1}{a}\sin\left(ax\right)+C, where a=\frac{\pi}{2}. Divide 1 by \frac{\pi}{2}. Evaluate the definite integral.

##  Final answer to the problem

$\frac{2}{\pi}$

$0.63662$

##  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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5
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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