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Integrate the function $x\sin\left(x\right)^2$ from $\frac{\pi }{2}$ to $\frac{5\pi }{2}$

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asinh
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Final Answer

$14.02749$
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Step-by-step Solution

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Simplifying

$\int_{\frac{\pi}{2}}^{\frac{5\pi}{2}} x\sin\left(x\right)^2dx$

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

$\int_{\frac{\pi}{2}}^{\frac{5\pi}{2}} x\sin\left(x\right)^2dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function xsin(x)^2 from pi/2 to (5*pi)/2. Simplifying. Apply the trigonometric identity: \sin\left(\theta \right)^2=\frac{1-\cos\left(2\theta \right)}{2}. Multiplying the fraction by x. Take the constant \frac{1}{2} out of the integral.

Final Answer

$14.02749$

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Function Plot

Plotting: $x\sin\left(x\right)^2$

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7
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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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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

9. See formulas

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