What is the integral from 0 to pi/4 of sin(t)+cos(t) ?

The integral from 0 to pi/4 of sin(t)+cos(t) is 1

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integral from 0 to pi/4 of sin(t)+cos(t)

\int_{0}^{\frac{π}{4}} sin (t) + cos (t) d t

1

Solution steps

\int_{0}^{\frac{π}{4}} sin (t) + cos (t) d t

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}^{\frac{π}{4}} sin (t) d t + \int_{0}^{\frac{π}{4}} cos (t) d t

\int_{0}^{\frac{π}{4}} sin (t) d t = - \frac{1}{2} + 1

\int_{0}^{\frac{π}{4}} cos (t) d t = \frac{1}{2}

= - \frac{1}{2} + 1 + \frac{1}{2}

Simplify

= 1

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What is the integral from 0 to pi/4 of sin(t)+cos(t) ?
The integral from 0 to pi/4 of sin(t)+cos(t) is 1