Integrate the function $\left(t+3\right)\cos\left(\frac{\pi n}{3}t\right)$ from $-3$ to 0

Step-by-step Solution

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Final answer to the problem

$\frac{2273749.9039604-2273749.9039604\cos\left(\frac{354.9250769}{112.9761608}n\right)}{2493445.7843449n^2}$
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Step-by-step Solution

How should I solve this problem?

  • Integrate using trigonometric identities
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.
1

Take $\frac{\pi }{3}$ out of the fraction

$\int_{-3}^{0}\left(t+3\right)\cos\left(\frac{118.308359}{112.9761608}nt\right)dt$

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$\int_{-3}^{0}\left(t+3\right)\cos\left(\frac{118.308359}{112.9761608}nt\right)dt$

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Integrate the function (t+3)cos((npi)/3t) from -3 to 0. Take \frac{\pi }{3} out of the fraction. We can solve the integral \int\left(t+3\right)\cos\left(\frac{118.308359}{112.9761608}nt\right)dt 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.

Final answer to the problem

$\frac{2273749.9039604-2273749.9039604\cos\left(\frac{354.9250769}{112.9761608}n\right)}{2493445.7843449n^2}$

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Function Plot

Plotting: $\left(t+3\right)\cos\left(\frac{\pi n}{3}t\right)$

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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

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