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# Integrate the function $\sin\left(2x\right)$ from 0 to $3^{3x}$

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##  Final answer to the problem

$-\frac{1}{2}\cos\left(2\cdot 3^{3x}\right)+\frac{1}{2}$
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##  Step-by-step Solution 

How should I solve this problem?

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• 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
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Can't find a method? Tell us so we can add it.
1

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

$\left[- \left(\frac{1}{2}\right)\cos\left(2x\right)\right]_{0}^{3^{3x}}$

Learn how to solve problems step by step online.

$\left[- \left(\frac{1}{2}\right)\cos\left(2x\right)\right]_{0}^{3^{3x}}$

Learn how to solve problems step by step online. Integrate the function sin(2x) from 0 to 3^(3x). 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. Simplify the expression.

##  Final answer to the problem

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

##  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

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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

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