Prouve that $\mathcal{F}\{\frac{dx(t)}{dt}\} = 2i\pi f \mathcal{F}\{x(t)\}$
68854
Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
63237
Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
109790
Finding the value of $\int_0^{\pi/2} \frac{dt}{1+(\tan(x))^{\sqrt{2}}}$
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
151063
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
116946
Ordinary differential equation $y'(t)=\sin(f(t,y))$
133990
How prove this $\int_{a}^{b}f(x)dx=\frac{1}{2}(b-a)[f(a)+f(b)]-\frac{1}{12}(b-a)^3f''(\xi)$
50844
How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
141516
Solve $\int_0^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt$
62110
Proving a function $\frac{1}{2y}\int_{x-y}^{x+y} f(t) dt=f(x)$ is a linear polynomial
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
105790
What is the Fourier Transform of $f'(x)/x$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
34790
Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
28053
Integral of $\sin(e^t)dt$