• anonymous
Fool's problem of the day, Wonderful Integrals: 1. Evaluate: $$\huge \int \frac{\sin x}{\sqrt{1+\sin x}}$$ 2. Prove $$\huge \int \limits_{0}^{\frac \pi 2}\frac{x}{\sin x+\cos x}dx = \frac{\pi}{2\sqrt{2}} \ln (\sqrt{2} +1)$$ 3. Prove $$\int \limits_{0} ^1 \sqrt{(1+x)(1+x^3)} \; dx \le \sqrt{\frac{15}{8}}$$ 4. Let $$a,b, c$$ be non-zero real numbers, such that $$\int \limits_{0} ^1 (1+ \cos ^8 x)(ax^2 bx +c) \; dx = \int \limits_{0} ^2 (1+ \cos ^8 x)(ax^2 bx +c) \; dx$$. Then show that the quadratic equation $$ax^2 +bx+c=0$$ has one root in $$(1,2)$$ [Solved by @Mr.Math] PS: First two are probably very easy! ;) @TuringTest Time for you solve my problem of the day! Between I would only accept all the solutions from you ;) Good luck!
Mathematics
• Stacey Warren - Expert brainly.com
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