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

The integral from 0 to pi of |sin(x)-cos(x)| is 2sqrt(2)

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

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

22

Decimal Notation

2.82842 \dots

Solution steps

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

Eliminate Absolutes

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

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

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

= 2 - 1 + 1 + 2

Simplify

= 22

\int_{0}^{π} 2 x cos (x) d x

\int_{0}^{4} x sin (x) d x

\int_{0}^{3} 5 (1 - e^{y}) d y

\int_{\frac{π}{3}}^{π} cos (x + \frac{π}{3}) d x

\int_{0}^{1} 17 x^{3} 1 - x^{2} d x

What is the integral from 0 to pi of |sin(x)-cos(x)| ?
The integral from 0 to pi of |sin(x)-cos(x)| is 2sqrt(2)