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Alice
Alice
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I have an increasing function $H:[0,\infty)\to[0,\infty)$, and a function G defined as $$G(t)=\int_0^t H(s)ds.$$

The function $H$ has the proprty that $H(0)=0$.

I need a numerical method to find t, given that I know $G(t)=x$ for some $x\in[0,\infty)$.

I have seen a similar question asked here: Numerical Solution to Inverse Integral (Pseudo Random Number Generation) but there was no reference and I'm not sure I understand why it works.

I have an increasing function $H:[0,\infty)\to[0,\infty)$, and a function G defined as $$G(t)=\int_0^t H(s)ds.$$

I need a numerical method to find t, given that I know $G(t)=x$ for some $x\in[0,\infty)$.

I have seen a similar question asked here: Numerical Solution to Inverse Integral (Pseudo Random Number Generation) but there was no reference and I'm not sure I understand why it works.

I have an increasing function $H:[0,\infty)\to[0,\infty)$, and a function G defined as $$G(t)=\int_0^t H(s)ds.$$

The function $H$ has the proprty that $H(0)=0$.

I need a numerical method to find t, given that I know $G(t)=x$ for some $x\in[0,\infty)$.

I have seen a similar question asked here: Numerical Solution to Inverse Integral (Pseudo Random Number Generation) but there was no reference and I'm not sure I understand why it works.

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Alice
Alice
  • 41
  • 4

Numerically inverting an integral

I have an increasing function $H:[0,\infty)\to[0,\infty)$, and a function G defined as $$G(t)=\int_0^t H(s)ds.$$

I need a numerical method to find t, given that I know $G(t)=x$ for some $x\in[0,\infty)$.

I have seen a similar question asked here: Numerical Solution to Inverse Integral (Pseudo Random Number Generation) but there was no reference and I'm not sure I understand why it works.