Exercise
$\int_{\frac{\pi}{6}}^{\frac{5\pi}{6}}\left(1-senx\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function 1-sin(x) from pi/6 to (5pi)/6. Expand the integral \int_{\frac{\pi }{6}}^{\frac{5\pi }{6}}\left(1-\sin\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{\frac{\pi }{6}}^{\frac{5\pi }{6}}1dx results in: \frac{5\pi }{6}-\frac{\pi }{6}. Gather the results of all integrals. Combine fractions with common denominator 6.
Integrate the function 1-sin(x) from pi/6 to (5pi)/6
Final answer to the exercise
$\frac{2\pi }{3}-\cos\left(\frac{\pi }{6}\right)+\cos\left(\frac{5\pi }{6}\right)$