Consider this simple equation $$ \tau(t)=\int\frac{dt}{a(t)},$$ where $\tau$ and $a$ are functions of $t$. Now, from this equation, how can I calculate $a(\tau)$ ?
2026-03-27 07:30:49.1774596649
Invert a function containing integration term
23 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in INTEGRATION
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- How to integrate $\int_{0}^{t}{\frac{\cos u}{\cosh^2 u}du}$?
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- How to find the unit tangent vector of a curve in R^3
- multiplying the integrands in an inequality of integrals with same limits
- Closed form of integration
- Proving smoothness for a sequence of functions.
- Random variables in integrals, how to analyze?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Which type of Riemann Sum is the most accurate?
Related Questions in INVERSE
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Proving whether a matrix is invertible
- Proof verification : Assume $A$ is a $n×m$ matrix, and $B$ is $m×n$. Prove that $AB$, an $n×n$ matrix is not invertible, if $n>m$.
- Help with proof or counterexample: $A^3=0 \implies I_n+A$ is invertible
- Show that if $a_1,\ldots,a_n$ are elements of a group then $(a_1\cdots a_n)^{-1} =a_n^{-1} \cdots a_1^{-1}$
- Simplifying $\tan^{-1} {\cot(\frac{-1}4)}$
- Invertible matrix and inverse matrix
- show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$
- Inverse matrix for $M_{kn}=\frac{i^{(k-n)}}{2^n}\sum_{j=0}^{n} (-1)^j \binom{n}{j}(n-2j)^k$
- What is the determinant modulo 2?
Related Questions in INVERSE-FUNCTION
- Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$
- Combination of functions and their inverses.
- Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring
- Find the greatest and least values of $(\sin^{-1}x)^2+(\cos^{-1}x)^2$
- Is it always possible to rearrange an equation desirably?
- Only bijective mappings are invertible. Clarifying proof.
- Relating the roots of quadratic to an inverse trigonometric functions' question
- Derive the conditions for $\tan^{-1}\frac{a\cos x-b\sin x}{b\cos x+a\sin x}=\tan^{-1}\frac{a}{b}-x$
- Why is the inverse of the derivative of f not the actual derivative of the inverse of f?
- $\ {\sin}^{-1}{(x)} $ equation and function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
$\tau'(t)=\frac 1 {a(t)}$ so $a(t)=\frac 1 {\tau'(t)}$.