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Step-by-step Solution

Integrate ycos(y) from 0 to 4

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ln
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sin
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csc

asin
acos
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sinh
cosh
tanh
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sech
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asinh
acosh
atanh
acoth
asech
acsch

Answer

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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 $du$

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

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Answer

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

Main topic:

Integration by parts

Used formulas:

3. See formulas

Time to solve it:

~ 0.43 seconds