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Integrate the function $\left(\pi -x\right)\cos\left(nx\right)$ from 0 to $\pi $

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{2.1415927\sin\left(\pi n\right)}{n}+\frac{-\cos\left(\pi n\right)+1}{n^2}$
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Step-by-step Solution

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Learn how to solve improper integrals problems step by step online. Integrate the function (pi-x)cos(nx) from 0 to pi. We can solve the integral \int\left(\pi -x\right)\cos\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 or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.

Final answer to the problem

$\frac{2.1415927\sin\left(\pi n\right)}{n}+\frac{-\cos\left(\pi n\right)+1}{n^2}$

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Function Plot

Plotting: $\left(\pi -x\right)\cos\left(nx\right)$

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0
a
b
c
d
f
g
m
n
u
v
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x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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Main Topic: Improper Integrals

An improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number that is not part of the function's domain, or infinity.

Used Formulas

See formulas (4)

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