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Question

How many of the following statements are correct?

1. x2dx=x3

2. sinxdx=cosx

3. exdx=ln x

4. 1xdx=x0

5. tanxdx=sec2x


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Solution

We saw that integration is inverse process of differentiation. So to check if the following statements are correct, we will differentiate the function on the RHS, and check if we get the function on the LHS in integral.

  1. Derivative of x3=3x2 So the first relation is not correct.
  2. Derivative of cosx=sinx in correct
  3. Derivative of lnx=1x incorrect
  4. Derivative of x0= Derivative of 1=0 Incorrect
  5. Derivative of sec2x=2 secx secx tanx Incorrect
    So, all the integrals given are wrong.

=> answer = 0

It’s also important to know the integral of all these functions for solving other questions.

Correct relation is as follows

1. x2=x3/3+C
2. sinx=cosx+C
3. ex=ex+C
4. 1x=ln|x|+C
5. tanx=ln|secx|+C

You have seen all the integrals except the last one, which we will see in standard formulae - 2


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