What is the integral from 0 to pi/2 of sin(x)+cos(x) ?

The integral from 0 to pi/2 of sin(x)+cos(x) is 2

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integral from 0 to pi/2 of sin(x)+cos(x)

\int_{0}^{\frac{π}{2}} sin (x) + cos (x) d x

2

Solution steps

\int_{0}^{\frac{π}{2}} 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}^{\frac{π}{2}} sin (x) d x + \int_{0}^{\frac{π}{2}} cos (x) d x

\int_{0}^{\frac{π}{2}} sin (x) d x = 1

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

= 1 + 1

Simplify

= 2

\int_{0}^{2} 4 x - x^{2} d x

\int_{- π}^{π} sin (x) sin (2 x) d x

\int_{5}^{5} 4 x d x

\int_{1}^{2} \frac{1}{x ^{2} - x} d x

\int_{0}^{t} cos (t) d t

What is the integral from 0 to pi/2 of sin(x)+cos(x) ?
The integral from 0 to pi/2 of sin(x)+cos(x) is 2