Q. 14.0( 235 Votes )

Find an anti-derivative (or integral) of the following functions by the method of inspection.

sin 2x

Answer :

Method: To find the anti derivative of a function by inspection 
Steps: 1. In this method we look for a function whose derivative is the given function. For Example: if we need to find anti derivative of x2, we know that derivative of x3 is 3x2. Therefore, the variable terms comes out to be the same.
2. After that balance out the coefficients of variables by dividing and multiplying suitable terms. From above example if [we divide x3 by 3 we will get the answer as x2. Hence, we can say that anti derivative of xis x3/3.

Now, similarly,

We know that


Therefore, the anti-derivative of sin2x is

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