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

## Step-by-step Solution

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###  Videos

$\frac{3}{2}$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

Cancel like terms $x^2$ and $-x^2$

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

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

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

Learn how to solve definite integrals problems step by step online. Integrate the function x^2+x-x^2 from -1 to 2. Cancel like terms x^2 and -x^2. Applying the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, in this case n=1. Evaluate the definite integral. Simplify the expression inside the integral.

$\frac{3}{2}$

$1.5$

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

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5
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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

~ 0.02 s

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