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Integrate the function $\sin\left(x\right)^2-x\sin\left(x^2\right)$ from 0 to $1$

Step-by-step Solution

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Final Answer

$\frac{20}{467}$
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Step-by-step Solution

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Expand the integral $\int_{0}^{1}\left(\sin\left(x\right)^2-x\sin\left(x^2\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{0}^{1}\sin\left(x\right)^2dx+\int_{0}^{1}-x\sin\left(x^2\right)dx$

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

$\int_{0}^{1}\sin\left(x\right)^2dx+\int_{0}^{1}-x\sin\left(x^2\right)dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function sin(x)^2-xsin(x^2) from 0 to 1. Expand the integral \int_{0}^{1}\left(\sin\left(x\right)^2-x\sin\left(x^2\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1}\sin\left(x\right)^2dx results in: 0.272676. The integral \int_{0}^{1}-x\sin\left(x^2\right)dx results in: -\frac{77}{335}. Gather the results of all integrals.

Final Answer

$\frac{20}{467}$

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 (sinx^2+-1x)dx from 0 to 1 using basic integralsSolve integral of (sinx^2+-1x)dx from 0 to 1 using u-substitutionSolve integral of (sinx^2+-1x)dx from 0 to 1 using integration by parts

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Function Plot

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

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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

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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

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