Integrate the function $\sin\left(2x\right)$ from 0 to $\pi $

Step-by-step Solution

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Final answer to the problem

$-\frac{1}{2}\cos\left(2\pi \right)- \left(-\frac{1}{2}\right)\cos\left(2\cdot 0\right)$
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Step-by-step Solution

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  • Integrate by partial fractions
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  • Weierstrass Substitution
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  • Integrate using basic integrals
  • Product of Binomials with Common Term
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1

Apply the formula: $\int\sin\left(ax\right)dx$$=-\left(\frac{1}{a}\right)\cos\left(ax\right)+C$, where $a=2$

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

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

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

Final answer to the problem

$-\frac{1}{2}\cos\left(2\pi \right)- \left(-\frac{1}{2}\right)\cos\left(2\cdot 0\right)$

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Function Plot

Plotting: $\sin\left(2x\right)$

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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

How to improve your answer:

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

Used Formulas

See formulas (1)

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