What is the integral from 1 to 7 of |sin(x)| ?

The integral from 1 to 7 of |sin(x)| is 4+cos(1)-cos(7)

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integral from 1 to 7 of |sin(x)|

\int_{1}^{7} ∣ sin (x) ∣ d x

4 + cos (1) - cos (7)

Decimal Notation

3.78640 \dots

Solution steps

\int_{1}^{7} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{1}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{7} sin (x) d x

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

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{7} sin (x) d x = - cos (7) + 1

= 1 + cos (1) + 2 - cos (7) + 1

Simplify

= 4 + cos (1) - cos (7)

\int_{0}^{1} (1 - x) sin (nπ x) d x

\int_{\frac{π}{2}}^{\frac{3 π}{2}} x sin (x) d x

\int_{2}^{3} \frac{x}{1 - x ^{2}} d x

\int_{2}^{6} x d x

\int_{1}^{3} (2 x - 1) d x

What is the integral from 1 to 7 of |sin(x)| ?
The integral from 1 to 7 of |sin(x)| is 4+cos(1)-cos(7)