What is the integral from 0 to 2 of x*sin(x) ?

The integral from 0 to 2 of x*sin(x) is sin(2)-2cos(2)

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integral from 0 to 2 of x*sin(x)

\int_{0}^{2} x \cdot sin (x) d x

sin (2) - 2 cos (2)

Decimal Notation

1.74159 \dots

Solution steps

\int_{0}^{2} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{2}

= [- x cos (x) - \int - cos (x) d x]_{0}^{2}

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{0}^{2}

Simplify

= [- x cos (x) + sin (x)]_{0}^{2}

Compute the boundaries:

sin (2) - 2 cos (2)

= sin (2) - 2 cos (2)

\int_{0}^{4} \frac{1}{5} e^{\frac{- x}{5}} d x

\int_{0}^{2 π} 7 t \cdot 2 d t

\int_{0.17}^{0.13} (4.5 \cdot 1 0^{5}) d x

\int_{0}^{- 2} [x^{3} - 2 x] d x

What is the integral from 0 to 2 of x*sin(x) ?
The integral from 0 to 2 of x*sin(x) is sin(2)-2cos(2)