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# Integrate the function $\left(3x\right)^3$ from $1$ to $-121$

## Step-by-step Solution

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##  Step-by-step Solution 

Problem to solve:

$\int_{1}^{-121}\left(3x\right)^3dx$

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1

Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: $\int_a^bf(x)dx=-\int_b^af(x)dx$

$-\int_{-121}^{1}\left(3x\right)^3dx$

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

$-\int_{-121}^{1}\left(3x\right)^3dx$

Learn how to solve definite integrals problems step by step online. Integrate the function (3x)^3 from 1 to -121. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. Rewrite the expression \left(3x\right)^3 inside the integral in factored form. The integral of a function times a constant (27) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 3.

$1446922440$

##  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((3x)^3)dx&1&-121 using partial fractionsSolve int((3x)^3)dx&1&-121 using basic integralsSolve int((3x)^3)dx&1&-121 using u-substitutionSolve int((3x)^3)dx&1&-121 using integration by partsSolve int((3x)^3)dx&1&-121 using trigonometric substitution

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1
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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

~ 0.04 s

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