Prove that there is a constant C such that
\(\displaystyle \sup_{A<B} \int_A^B \sin(x^2+ yx) \, dx \le C\)
for all y.
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Tag Archives: integral
2010-11 Integral Equation
Let z be a real number. Find all solutions of the following integral equation: \(f(x)=e^x+z \int_0^1 e^{x-y} f(y)\,dy\) for 0≤x≤1.
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2009-22 Integral and Limit
Evaluate the following limit:
\(\displaystyle \lim_{\varepsilon\to 0}\int_0^{2\varepsilon} \log\left(\frac{|\sin t-\varepsilon|}{\sin \varepsilon}\right) \frac{dt}{\sin t}\).
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