👉 Try now NerdPal! Our new math app on iOS and Android

Find the integral $\frac{1}{\pi }\int_{-\pi }^{\pi } x\sin\left(nx\right)$

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

Final Answer

$\frac{-2\cos\left(\pi n\right)}{n}+\frac{\frac{2}{\pi}\sin\left(\pi n\right)}{n^2}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

We can solve the integral $\int x\sin\left(nx\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve differential calculus problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve differential calculus problems step by step online. Find the integral 1/piint(xsin(nx))dx&-pi&pi. We can solve the integral \int x\sin\left(nx\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Final Answer

$\frac{-2\cos\left(\pi n\right)}{n}+\frac{\frac{2}{\pi}\sin\left(\pi n\right)}{n^2}$

Explore different ways to solve this problem

Give us your feedback!

Function Plot

Plotting: $\frac{-2\cos\left(\pi n\right)}{n}+\frac{\frac{2}{\pi}\sin\left(\pi n\right)}{n^2}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account