Try now NerdPal! Our new app on iOS and Android

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

## 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

$\frac{3}{2}-3$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

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

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

Learn how to solve simplification of algebraic fractions problems step by step online.

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

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

$\frac{3}{2}-3$

$-1.5$

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

Simplification of algebraic fractions

~ 0.04 s

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

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