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

The integral from 0 to pi/4 of sin(x)-cos(x) is -sqrt(2)+1

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integral from 0 to pi/4 of sin(x)-cos(x)

\int_{0}^{\frac{π}{4}} sin (x) - cos (x) d x

- 2 + 1

Decimal

- 0.41421 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 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}{4}} sin (x) d x - \int_{0}^{\frac{π}{4}} cos (x) d x

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

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

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

Simplify

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

= - 2 + 1

\int_{0}^{12} \frac{1}{36} (x (12 - x)) d x

\int_{0}^{π} (cos (x))^{2} d x

\int_{0}^{4} \frac{x ^{2}}{8} d x

\int_{0}^{\frac{π}{2}} 4 cos (x) d x

\int_{- 2}^{4} - x^{2} + 2 x + 8 d x

What is the integral from 0 to pi/4 of sin(x)-cos(x) ?
The integral from 0 to pi/4 of sin(x)-cos(x) is -sqrt(2)+1