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Find the integral $\int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx$

Step-by-step Solution

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Solution

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Final Answer

$x\sin\left(y\right)+y\cos\left(x\right)+C_0$
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Step-by-step Solution

Problem to solve:

$\int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx$

Specify the solving method

1

Expand the integral $\int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\sin\left(y\right)dx+\int-y\sin\left(x\right)dx$

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

$\int\sin\left(y\right)dx+\int-y\sin\left(x\right)dx$

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Unlock the first 2 steps of this solution.

Learn how to solve integral calculus problems step by step online. Find the integral int(sin(y)-ysin(x))dx. Expand the integral \int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sin\left(y\right)dx results in: x\sin\left(y\right). The integral \int-y\sin\left(x\right)dx results in: y\cos\left(x\right). Gather the results of all integrals.

Final Answer

$x\sin\left(y\right)+y\cos\left(x\right)+C_0$

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 int(sin(y)-ysin(x))dx using basic integralsSolve int(sin(y)-ysin(x))dx using u-substitutionSolve int(sin(y)-ysin(x))dx using integration by parts

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0
a
b
c
d
f
g
m
n
u
v
w
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:

Integral Calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.05 s

Related topics:

Integral CalculusCalculus

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