What is the integral from 0 to 1 of sin(x)-xsin(x) ?

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

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integral from 0 to 1 of sin(x)-xsin(x)

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

- sin (1) + 1

Decimal Notation

0.15852 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{1} sin (x) d x = - cos (1) + 1

\int_{0}^{1} x sin (x) d x = sin (1) - cos (1)

= - cos (1) + 1 - (sin (1) - cos (1))

Simplify

= - sin (1) + 1

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\int_{0}^{\frac{π}{6}} sin (θ) d θ

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