Prove the statement for definite integral
47498
Integration and theorems on continuous functions
67830
Evalute the definite integral: $\int_{0}^{3} (x^2+1) d[x]$
64314
Proof of certain Gaussian integral form
132448
Prove that: $\int_0^{n\pi}f(\cos^2(x))\,dx=n\int_0^{\pi}f(\cos^2(x))\,dx?$
116044
Can one prove $\int f > 0$ for $f > 0$ without Lebesgue integration?
56867
Convergence proof that involves integral
141852
Prove that $2\int_a^b \int_a^x f(x)f(y) \, dy \, dx = \left[ \int_a^b f(x) \, dx \right]^2$
107146
How can i prove this problem about Cauchy integral?
49408
Proof of the derivative of ln(x)
97643
Prove that:$f(f(x)) = x^2 \implies \int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}$
78174
How prove this inequality $\left(\int_{0}^{1}f(x)dx\right)^2\le\frac{1}{12}\int_{0}^{1}|f'(x)|^2dx$
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
154183
Proof of a Ramanujan Integral
87149
Prove directly from the definition of the Ito's integral
93276
A question on applying Residue Theorem to definite real integral
48408
Definite Integral of $\sin(\sin x)$
158180
An inequality of $\int_0^1 |f(x)|dx$