Question

3. (4x3 -5x2 +6x +9) dx

Answer 1

Consider the given integral,

I= ∫ 1 2 ( 4 x 3 −5 x 2 +6x+9 )dx

Now, integrate the function,

∫ ( 4 x 3 −5 x 2 +6x+9 )dx =( 4 x 3+1 3+1 −5( x 2+1 2+1 )+6 x 1+1 1+1 +9x ) =( x 4 −5( x 3 3 )+3 x 2 +9x ) =F( x )

By fundamental theorem of calculus, we get

I=F( 2 )−F( 1 ) =( ( 2 ) 4 −5( ( 2 ) 3 3 )+3 ( 2 ) 2 +9( 2 )−( ( 1 ) 4 − 5 3 ( 1 ) 2 +3 ( 1 ) 2 +9( 1 ) ) ) =16− 40 3 +12+18−1+ 5 3 −3−9 = 64 3

Thus, the solution of integral is 64 3 .