Why $\int _c^df^{-1}\left(y\right)\:dy+\int _a^b\:f\left(x\right)dx=b\cdot d-a\cdot c$?
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
73504
Why $(a+d)(b+c)$ equals $-16$?
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
68746
What is $f(f^{-1}(A))$?
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
79575
The sum of integrals of a function and its inverse: $\int_{0}^{a}f+\int_{0}^{f(a)}f^{-1}=af(a)$
10366
Why do we not include $c$ in the computation of the definite integral?
95908
What is the meaning of $\exp(\,\cdot\,)$?
93610
What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?
34907
Show that $\int_{0}^{1}\{P(x)\}^{2}\,dx = (n + 1)^{2}\left(\int_{0}^{1}P(x)\,dx\right)^{2}$
68854
Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
128921
Why define $(\nabla^2F)(X,Y)=\nabla_X(\nabla_YF)-(\nabla_{\nabla_XY}F)$?
55364
Show $au_x+bu_y=f(x,y)$ gives $u(x,y)=(a^2+b^2)^{-\frac{1}{2}}\int_{L}fds +g(bx-ay)$ if $a\neq 0$.
138082
What are the coefficients in the expansion of $(x+y)(x+2y) \cdots (x+ny)$?
94499
What is $c + (-c)$?
140386
Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $