# Can one say "take an integral" instead of "calculate an integral"? What other options are there?

Russians often use the formulation "take an integral". Now I noticed it in an article, written by a Russian and I can't recall I have ever encountered it in English. Is it a possible alternative to the basic "calculate an integral"? What other options are there? "Evaluate", "find", ...?

• Take the integral is freshman college course Calculus 101 talk. You could perform the first derivative, but take is the standard instruction. Commented Jun 18, 2023 at 14:28
• Are you asking about academic mathematicians, or general members of the public? The usage among academics is likely to be distinct from other groups, should they have to do integrals. Commented Jun 18, 2023 at 16:28
• It's common enough when you are focusing on the range of a definite integral, eg. take the integral over -pi to +pi. Commented Jun 18, 2023 at 17:22
• I'm not sure why this was closed as 'opinion based'. If this is opinion based then so is every question on the site. Asking for what's generally accepted (or 'the most appropriate') is often just a question as to what is most frequent. Very much an on-topic question and one that makes this site useful. Commented Jun 19, 2023 at 13:39
• I asked this question on MESE a long time ago. Commented Jun 19, 2023 at 16:18

This transitive sense (most are!) of the highly polysemous verb 'take' is listed by Merriam-Webster:

take [verb] [transitive]:

11: ... (b) (1): to obtain as the result of a special procedure

• take the temperature
• take a census

Can the procedure be a mathematical one?

'Take the square root' is very commonly used; examples are:

• How do you find the square root of a perfect square? ... This tutorial shows you how to take the square root of 36. [Virtual Nerd]
• However, the easiest and most insightful way to take the square root of a complex number (as well as any higher order roots) is to use the geometric representation of the complex numbers. [University of Toronto Maths Network]

But it's used more often in algebraic rather than arithmetic contexts:

• ... solves the equation 2x²+3=75 by isolating x² and taking the square root of both sides. [Khan Academy]

'Calculate', 'work out' or 'find' are the more usual ways to express the finding of a numerical square root.

'Take logarithms' is again more usually found when solving equations:

2ˣ+3 = 137 ⇒ 2ˣ = 134

Taking logs to base 10

x log2 = log 134 [⇒ ⇒ x]

But when it comes to 'take the integral', there are many internet examples of this being used as a synonym for 'work out the integral'. Here is an example from Mathematics.SE:

• How do I take the integral of [a] complex power function with a non-integral power?

And one from Study.com

• How to take the integral of a factorial

However, I'd say 'calculate [the integral]' is the common choice where the answer will be numerical.

"Finding" an integral is both common and general. "Calculate" is possible, but often suggests that the answer will be a number, and "evaluate" also suggests this. "Simplifying" an expression which happens to be an integral is also possible.

If we already have an expression we can "take" its integral, or we can just "integrate" it.