The value of the integral int_{0}^{pi / 2} (s | vedclass

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(D) Let $I = \int_{0}^{\pi / 2} (\sin^{100} x - \cos^{100} x) dx$. Using the property $\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) dx$,we have: $I = \i

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(D) Let $I = \int_{0}^{\pi / 2} (\sin^{100} x - \cos^{100} x) dx$. Using the property $\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) dx$,we have: $I = \int_{0}^{\pi / 2} (\sin^{100}(\frac{\pi}{2} - x) - \cos^{100}(\frac{\pi}{2} - x)) dx$ $I = \int_{0}^{\pi / 2} (\cos^{100} x - \sin^{100} x) dx$ $I = -\int_{0}^{\pi / 2} (\sin^{100} x - \cos^{100} x) dx$ $I = -I$ $2I = 0$ $I = 0$.

The value of the integral $\int_{0}^{\pi / 2} (\sin^{100} x - \cos^{100} x) dx$ is

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