Try now NerdPal! Our new app on iOS and Android

# Integrate the function $x^2-1$ from $-1$ to $1$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

###  Videos

$-\frac{4}{3}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\int_{-1}^{1}\left(x^2-1\right)dx$

Specify the solving method

1

Expand the integral $\int_{-1}^{1}\left(x^2-1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{-1}^{1} x^2dx+\int_{-1}^{1}-1dx$

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

$\int_{-1}^{1} x^2dx+\int_{-1}^{1}-1dx$

Learn how to solve definite integrals problems step by step online. Integrate the function x^2-1 from -1 to 1. Expand the integral \int_{-1}^{1}\left(x^2-1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-1}^{1} x^2dx results in: \frac{2}{3}. The integral \int_{-1}^{1}-1dx results in: -2. Gather the results of all integrals.

$-\frac{4}{3}$

$-1.3333$

##  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(x^2-1)dx&-1&1 using partial fractionsSolve int(x^2-1)dx&-1&1 using basic integralsSolve int(x^2-1)dx&-1&1 using u-substitutionSolve int(x^2-1)dx&-1&1 using integration by partsSolve int(x^2-1)dx&-1&1 using trigonometric substitution

SnapXam A2

Go!
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

~ 0.04 s

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account