How do I find a function that is proportional to the definite integral of itself and a trigonometric function in a limited space?
127558
If $f(x)=x-\int^{\frac{\pi}{2}}_0f(x)\sin(x)dx$ find the explicit function for $f(x)$ in its simplest form
67655
Simpler way to compute a definite integral without resorting to partial fractions?
151063
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
144406
Integrating a difficult function (Numerically ?)
18967
Linear independence of $\sin(x)$ and $\cos(x)$
79684
Finding $\lim \limits_{x \to 0} \frac{1 - \cos x}{x}$, given $\lim \limits_{x \to 0} \frac{\sin x}{x} = 1$
142114
Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
91212
Evaluate $\int \cos^3 x\;\sin^2 xdx$
125523
How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?
90339
Integral involving Cosine function
80366
How to find integral's upper limit using optimize function without knowing the interval where it will occur
136738
Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists?
115469
Integral of Sinc Function Squared Over The Real Line
130668
Evaluating the integral with trigonometric integrand
29970
Bounds of $I=\int_0^1\frac{\sin x}{\sqrt x}$ and $J=\int_0^1\frac{\cos x}{\sqrt x}$?
127343
Trigonometric integral involving the fractional part function
98678
Finding the following definite and indefinite integrals