5 Most Beautiful Questions From Integral Calculus


Some people love solving math just for its own sake – they find beauty in mathematics. For them, math is not only used for application in physics or engineering. It’s just beautiful in itself – on its own – PURE, BEAUTIFUL.

The “beauty” can be found in equations, expressions and the flow that takes place when you form a solution. Such beauty can be found in the following questions.

If you’re a Calculus student or a math enthusiast – try out these 5 beautiful questions from Integral Calculus. I made these questions a long time ago and have received solutions for only two of them so far. See if you can solve them all.

Question #1


Question #2


Question #3


Question #4


Question #5


You can leave your answers as a comment here or mail them to me at dev@durofy.com

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About Author

Founder at Durofy. Blogs on technology & startups, runs a full service digital agency, teaches AP Calculus.


  1. Pingback: How should I solve the following Calculus questions considering IIT JEE preparations? - Quora

  2. For question #4 hv tried by simplifying the given integral up to integral{[Cos(taninv(1/square root1 x^c)]^2dx.again simplifying the expression tointegral{(1 x^2)/(2 x^2)}dx by letting tanm=1/sq rt(1 x^2) then (cos m)^2 =(1 x^2)/(2 x^2).hence(cos(taninv1/sqr1 x^2)=(1 x^2)/(2 x^2).finally integrating the simplified expressions i got the answer as x-0.5sqroot[taninv(x/sqroot2)] constant

  3. Question can easily be solved by simplify{x(pi 49)}^15/7 to x^15/7(pi 49)^15/7 then use substituion method(by letting x^pi 7=u and differentiate to get du=pix^(pi-1)dx.but pi-1=15/7 and continue to solve it.

  4. @Rishabh Dev
    Thanks Rishabh Dev. I have done question #1. I am quoting the first picture. What is the institution and city where the work is housed? for citing your work

  5. arka ..loves math on

    ans 1 is :(7/22)* (pi+49)^15/7*(1/pi^2)* (ln|x^(1/7)|) ..trick is .. just replace pi=22/7 in case of power of x^pi in denominator

      • Nice point! Though while solving Calculus problems, we usually see pi and e from a high level view and even logarithms and other values are treated as approximations as the aim of the problem is to test calculus concepts. However, what you pointed out is right and a small instruction can be added saying “Assume pi = 22/7” however, that would also serve as a big hint which was the reason why that was avoided.

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