integral from 0 to 2pi of (3+pi|sin(θ)|)

解答

\int_{0}^{2 π} (3 + π ∣ sin (θ) ∣) d θ

10 π

十进制

31.41592 \dots

求解步骤

\int_{0}^{2 π} 3 + π ∣ sin (θ) ∣ d θ

拿掉绝对值

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

\int_{0}^{π} 3 + π sin (θ) d θ = 5 π

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

= 5 π + 5 π

化简

= 10 π