# JEE 1981 Int Calc

So, we have this definite integral:

We find the indefinite integral as follows, by first finding the antiderivatives:
After this, we take the derivative:
And since we wanted the solution from the area of x = 0 to x = 1, we can ignore the second chunk, as it diverges and repeats infinitely. We only pay attention to the first two snippets, the 2x and the -x^3/3.

Hope this helped!

Note by Hunter Edwards
10 months, 3 weeks ago

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The answer to the integral given was $$1+e^{-1}$$ , can you help , it doesn't seems it matches with the series you gave, Btw., awesome approach!

- 10 months, 3 weeks ago

Thank you! I'll have to look into it - my calc is a bit rusty :p @Sumukh Bansal and @Chung Kevin, Any help?

- 10 months, 3 weeks ago