query: Evaluate $\iint dydx$ on the domain $0\leq r\leq1$, ${\pi}/{3}\leq\theta \leq{2\pi}/{3}$
positive_passages.docid: 149913
positive_passages.text: Evaluate $\iint dy\,dx;\frac{\pi}{4}\leq\theta \leq\frac{3\pi}{4};0\leq r\leq2$
negative_passages.docid: 87338
negative_passages.text: Find the value of a given integral sequence: $I_n=\int_{0}^{1}(1-x^2)^ndx$
negative_passages.docid: 67322
negative_passages.text: evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
negative_passages.docid: 146737
negative_passages.text: Integrate $\iiint_E z\,dx\,dy\,dz$ in $E=\lbrace(x,y,z) : x^2+y^2+z^2 \leq 4, z \leq 1 \rbrace$
negative_passages.docid: 110731
negative_passages.text: How to compute $\int_{0}^{1}\int_{0}^{1} \frac{x-y}{(x+y)^3} dxdy$
negative_passages.docid: 139742
negative_passages.text: Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
negative_passages.docid: 105707
negative_passages.text: A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
negative_passages.docid: 139419
negative_passages.text: Problem on the domain of the solution of a differential equation
negative_passages.docid: 19475
negative_passages.text: Evaluate$\int_{-2}^2\int_{y^2-3}^{5-y^2}dxdy$
negative_passages.docid: 44653
negative_passages.text: $(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$
negative_passages.docid: 88368
negative_passages.text: Evaluating $\int_0^1 \sqrt{1 + x ^4 } \, d x $
negative_passages.docid: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 84034
negative_passages.text: Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$
negative_passages.docid: 122556
negative_passages.text: Integral $\int\!\sqrt{\cot x}\,dx $
negative_passages.docid: 36586
negative_passages.text: Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
negative_passages.docid: 121845
negative_passages.text: Quotient of polynomials, PID but not Euclidean domain?
negative_passages.docid: 157960
negative_passages.text: How can I prove the existence of two values in a given domain Mean value theorem?