how to numerically divide two unequal vector in R

I have a formula as:

\int_a^b \frac{exp(\Delta(G(t))} {D(t)} dt

in the above formula Delta(G) is a vector of 300 rows and 2 columns (Energy vs. Time) and D(t) is a vector of 30 rows and 2 columns (Diffusion vs. Time).

To solve this integral I have tried many strategies such as:

1- Fit an equation to D(t) named F1.
2- Fit another equation to Exponential named F2.
3- Divide F2 into F1 to give us F3.
4- Integrate F3 (from library 'stats').

But my solution result is far away from experimental result. I think my solution is not correct.

Plz, Could anyone elaborate on how to solve this in R.

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