What is the integral from 0 to x of xsin(y) ?

The integral from 0 to x of xsin(y) is x(-cos(x)+1)

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integral from 0 to x of xsin(y)

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

x (- cos (x) + 1)

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

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

Compute the boundaries:

- cos (x) + 1

= x (- cos (x) + 1)

\int_{- 1}^{3} 9 - x^{2} d x

\int_{0}^{1} (x^{3} - x) d x

\int_{2}^{x} \frac{1}{1 + t ^{4}} d t

\int_{- 2}^{2} 8 - 2 x^{2} d x

What is the integral from 0 to x of xsin(y) ?
The integral from 0 to x of xsin(y) is x(-cos(x)+1)