What is the integral from 0 to 20 of x+sin(x) ?

The integral from 0 to 20 of x+sin(x) is -cos(20)+201

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integral from 0 to 20 of x+sin(x)

\int_{0}^{20} x + sin (x) d x

- cos (20) + 201

Decimal Notation

200.59191 \dots

Solution steps

\int_{0}^{20} 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}^{20} x d x + \int_{0}^{20} sin (x) d x

\int_{0}^{20} x d x = 200

\int_{0}^{20} sin (x) d x = - cos (20) + 1

= 200 - cos (20) + 1

Simplify

= - cos (20) + 201

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What is the integral from 0 to 20 of x+sin(x) ?
The integral from 0 to 20 of x+sin(x) is -cos(20)+201