What is the integral from 4 to 10 of |sin(x)| ?

The integral from 4 to 10 of |sin(x)| is 4+cos(10)-cos(4)

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integral from 4 to 10 of |sin(x)|

\int_{4}^{10} ∣ sin (x) ∣ d x

4 + cos (10) - cos (4)

Decimal

3.81457 \dots

Solution steps

\int_{4}^{10} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{4}^{2 π} - sin (x) d x + \int_{2 π}^{3 π} sin (x) d x + \int_{3 π}^{10} - sin (x) d x

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

\int_{2 π}^{3 π} sin (x) d x = 2

\int_{3 π}^{10} - sin (x) d x = cos (10) + 1

= 1 - cos (4) + 2 + cos (10) + 1

Simplify

= 4 + cos (10) - cos (4)

\int_{1}^{5} 4 d x

\int_{1}^{e} \frac{ln ( x )}{2 x} d x

\int_{2}^{4} (3 x - 1 + 2 x^{2}) d x

\int_{0}^{1} 4 x e^{- 2 x} d x

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

What is the integral from 4 to 10 of |sin(x)| ?
The integral from 4 to 10 of |sin(x)| is 4+cos(10)-cos(4)