2.5) \(\displaystyle \displaystyle{ \int_0^{\frac{\pi}{2}}\, }\) \(\displaystyle \dfrac{\sin^2(x)}{\sin^2(x)\, +\, \sin(x)\, -\, \cos(x)\, +\, \cos^2(x)}\, dx\)
Find the integral using the following formula:
. . . . .\(\displaystyle \displaystyle{ \int_0^{\frac{\pi}{2}}\, }\) \(\displaystyle f\left(\sin(x)\right)\, dx\, =\,\) \(\displaystyle \displaystyle{ \int_0^{\frac{\pi}{2}}\, }\) \(\displaystyle f\left(\cos(x)\right)\, dx\)
Can you show me how to solve this by using the formula? The answer is \(\displaystyle \dfrac{2\pi}{3\sqrt{3\,}}\, \approx\, 1.21\)
Find the integral using the following formula:
. . . . .\(\displaystyle \displaystyle{ \int_0^{\frac{\pi}{2}}\, }\) \(\displaystyle f\left(\sin(x)\right)\, dx\, =\,\) \(\displaystyle \displaystyle{ \int_0^{\frac{\pi}{2}}\, }\) \(\displaystyle f\left(\cos(x)\right)\, dx\)
Can you show me how to solve this by using the formula? The answer is \(\displaystyle \dfrac{2\pi}{3\sqrt{3\,}}\, \approx\, 1.21\)
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