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# Integrate the function $x$ from $4$ to $2$

## Step-by-step Solution

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asinh
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###  Videos

$-6$
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##  Step-by-step Solution 

Problem to solve:

$\int_{4}^{2} xdx$

Specify the solving method

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: $\int_a^bf(x)dx=-\int_b^af(x)dx$

$-\int_{2}^{4} xdx$

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

$-\int_{2}^{4} xdx$

Learn how to solve definite integrals problems step by step online. Integrate the function x from 4 to 2. 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. 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.

$-6$

##  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 integral of xdx from 4 to 2 using partial fractionsSolve integral of xdx from 4 to 2 using u-substitutionSolve integral of xdx from 4 to 2 using integration by partsSolve integral of xdx from 4 to 2 using trigonometric substitution

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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

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