The value of the definite integral ∫$$a+2$$$$π$$$$a+5$$π$$/2$$ $$sin$$−$$1$$⁡$$($$$$cos$$⁡$$x)+$$$$cos$$−$$1$$⁡$$($$$$sin$$⁡$$x)dx$$ is equal to

Question

The value of the definite integral ∫$$a+2$$$$π$$$$a+5$$π$$/2$$ $$sin$$−$$1$$⁡$$($$$$cos$$⁡$$x)+$$$$cos$$−$$1$$⁡$$($$$$sin$$⁡$$x)dx$$ is equal to

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∵$$sin$$−$$1$$⁡$$($$$$cos$$⁡$$x)+$$$$cos$$−$$1$$⁡$$($$$$sin$$⁡$$x)$$ is periodic with period  $$2$$π then∫$$a+2$$$$π$$$$a+5$$π$$/2$$ $$sin$$−$$1$$⁡$$($$$$cos$$⁡$$x)+$$$$cos$$−$$1$$⁡$$($$$$sin$$⁡$$x)dx=$$∫$$0$$π$$/2$$ $$sin$$−$$1$$⁡$$($$$$cos$$⁡$$x)+$$$$cos$$−$$1$$⁡$$($$$$sin$$⁡$$x)dx=$$∫$$0$$π$$/2$$ $$sin$$−$$1$$⁡$$cos$$⁡π$$2$$−$$x+$$$$cos$$−$$1$$⁡$$sin$$⁡π$$2$$−$$xdx=$$∫$$0$$π$$/2$$ $$sin$$−$$1$$⁡$$sin$$⁡$$x+$$$$cos$$−$$1$$⁡$$cos$$⁡$$xdx=2$$∫$$0$$π$$/2$$ $$xdx=2x220$$$$π$$$$2=$$π$$24$$

The value of the definite integral $\int_{a + 2 π}^{a + 5 π / 2} \{\sin^{- 1} (\cos x) + \cos^{- 1} (\sin x)\} dx$ is equal to

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The value of the definite integral ∫a+2πa+5π/2 sin−1⁡(cos⁡x)+cos−1⁡(sin⁡x)dx is equal to

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The value of the definite integral $\int_{a + 2 π}^{a + 5 π / 2} \{\sin^{- 1} (\cos x) + \cos^{- 1} (\sin x)\} dx$ is equal to