integral from 0 to 5pi of |sin(x)|

解答

\int_{0}^{5 π} ∣ sin (x) ∣ d x

10

求解步骤

\int_{0}^{5 π} ∣ sin (x) ∣ d x

拿掉绝对值

= \int_{0}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{3 π} sin (x) d x + \int_{3 π}^{4 π} - sin (x) d x + \int_{4 π}^{5 π} sin (x) d x

\int_{0}^{π} sin (x) d x = 2

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{3 π} sin (x) d x = 2

\int_{3 π}^{4 π} - sin (x) d x = 2

\int_{4 π}^{5 π} sin (x) d x = 2

= 2 + 2 + 2 + 2 + 2

化简

= 10

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