Question

4. (ax + b)2

Answer 1

The function is given as,

y =  ( ax+b ) 2

We have to calculate the integral or anti-derivative of y.

Calculate the derivative of ( ax+b ) 3 ,

d dx ( ax+b ) 3 =  ( ax+b ) 3−1 ( 3 )× d( ax+b ) dx d dx ( ax+b ) 3 = ( ax+b ) 2 ( 3 )×( a⋅1 ) d dx ( ax+b ) 3 =3a ( ax+b ) 2 1 3a d dx ( ax+b ) 3 =  ( ax+b ) 2

Simplify further.

( ax+b ) 2 = 1 3a d dx [ ( ax+b ) 3 ]

Thus, the anti-derivative or integral of ( ax+b ) 2 is 1 3a ( ax+b ) 3 .