The antiderivatives of many functions either cannot be expressed or cannot be expressed easily in closed form (that is, in terms of known functions). Consequently, rather than evaluate definite integrals of these functions directly, we resort to various techniques of _______________ integration to approximate their values.

Given the antiderivatives of many ----------------- directly, we resort to various techniques of ________ integration to approximate their values.

We have to fill the blank in the sentence given with appropriate term.

Integration is a technique of finding a function from it's derivative.

Definite integral is the area under a curve between two limits. We have to find the answer by first putting upper limit and then lower limit. Then we have to subtract the answer from lower limit from the answer of upper limit.

In Indefinite integration we have not given any limits.

Numerical integration, a algorithm for calculating the numerical value of a definite integral.

Hence the term for the sentence is numerical integration.

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