Improper Integral Calculator

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There are different types of Integrals and improper integrals are one of them. Improper integrals are the integrals which have one of the limit or both the limits of integration as infinity. Improper integrals calculator is the instant online tool which can quickly evaluate an improper integral.


Example 1: Evaluate the integral of the given function, f(x) = 1/x3 with the limits of integration [1, ∞).

The integral notation of the above function is ->  ∫1∞ (1/x3)dx

The lower limit is 1, but the upper limit is ∞,

Hence -> we substitute the infinity with a finite‘t’ and take the limit approaching infinity.

 ∫1∞ (1/x3)dx = lim t_∞∫1t(1/x3)dx

limt_∞ [-1/2x2] |1t

-1/2 (limt_∞ [1/t2] – [1])

Now as ‘t’ approaches infinity, 1/t2 approaches ‘0’.

Hence ->  -1/2 * (-1) = 1/2




Example 2: Evaluate the integral of the given function, f(x) = 1/x2 with the limits of integration [1, ∞).

The integral notation of the above function is ->  ∫1∞ (1/x2)dx

The lower limit is 1, but the upper limit is ∞,

Hence->  we substitute the infinity with a finite‘t’ and take the limit approaching infinity.

-> ∫1∞ (1/x2)dx = lim t_∞ ∫1t(1/x2)dx

-> limt_∞ [-1/x] |1t

-> -1 (limt_∞ [1/t] – [1])

Now as ‘t’ approaches infinity, 1/tapproaches ‘0’.

Hence -> (-1) (-1) = 1

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