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

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##  Final Answer

$-\frac{4}{3}$
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##  Step-by-step Solution 

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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.

##  Final Answer

$-\frac{4}{3}$

##  Exact Numeric Answer

$-1.3333$

##  Explore different ways to solve this problem

SnapXam A2

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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

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