# Step-by-step Solution

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

undefined

## Step-by-step explanation

Problem to solve:

$\int_{0}^{4} y\cdot\cos\left(y\right)dy$
1

Use the integration by parts theorem to calculate the integral $\int y\cos\left(y\right)dy$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=y}\\ \displaystyle{du=dy}\end{matrix}$

undefined

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

$\int_{0}^{4} y\cdot\cos\left(y\right)dy$

### Main topic:

Integration by parts

~ 0.43 seconds