What is the integral from 0 to 1 of sin(x)+cos(x) ?

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

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integral from 0 to 1 of sin(x)+cos(x)

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

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

Decimal

1.30116 \dots

Solution steps

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

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

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

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

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