integral from 0 to (3pi)/2 of 6|sin(x)|

解答

\int_{0}^{\frac{3 π}{2}} 6 ∣ sin (x) ∣ d x

18

求解步骤

\int_{0}^{\frac{3 π}{2}} 6 ∣ sin (x) ∣ d x

拿掉绝对值

= \int_{0}^{π} 6 sin (x) d x + \int_{π}^{\frac{3 π}{2}} 6 (- sin (x)) d x

\int_{0}^{π} 6 sin (x) d x = 12

\int_{π}^{\frac{3 π}{2}} 6 (- sin (x)) d x = 6

= 12 + 6

化简

= 18

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