query: Finding the integral of a function between 0 to 1
positive_passages.docid: 15409
positive_passages.text: Calculate $\int_{0}^{1} (x-f(x))^{2016} dx$, given $f(f(x))=x$.
negative_passages.docid: 19526
negative_passages.text: Integral of an integral with variable limits
negative_passages.docid: 48314
negative_passages.text: Show that if a function is not negative and its integral is $0$ than the function is $0$
negative_passages.docid: 51216
negative_passages.text: Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$
negative_passages.docid: 65982
negative_passages.text: Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
negative_passages.docid: 78687
negative_passages.text: Integral with a discontinuity point
negative_passages.docid: 8289
negative_passages.text: Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$
negative_passages.docid: 32270
negative_passages.text: Integral depending on a parameter
negative_passages.docid: 144273
negative_passages.text: Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
negative_passages.docid: 112551
negative_passages.text: Demystify integration of $\int \frac{1}{x} \mathrm dx$
negative_passages.docid: 124463
negative_passages.text: Integral from $0$ to $\infty$ of $\ln(x)/e^x$
negative_passages.docid: 25797
negative_passages.text: Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
negative_passages.docid: 64743
negative_passages.text: How do I evaluate the integral $\int \frac{1}{x^3 -1}dx$
negative_passages.docid: 34855
negative_passages.text: Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$
negative_passages.docid: 67533
negative_passages.text: A question on integration
negative_passages.docid: 102156
negative_passages.text: Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx
negative_passages.docid: 17996
negative_passages.text: Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$