`int_1^2 (4x^3 - 3x^2 + 2x) dx` Evaluate the integral

You need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that:

`int_a^b f(x)dx = F(b) - F(a)`

`int_1^2(4x^3 - 3x^2 + 2x)dx = int_1^2(4x^3)dx - int_1^2 3x^2 dx + int_1^2 2x dx`

Evaluating each definite integral, using the formula `int x^n dx = (x^(n+1))/(n+1) + c` , yields:

`int_1^2(4x^3)dx = 4*(x^4)/4|_1^2 = 2^4 - 1^4 = 15`

`int_1^2 3x^2 dx =3x^3/3|_1^2 = 2^3 - 1^3 = 7`

`int_1^2...

You need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that:

`int_a^b f(x)dx = F(b) - F(a)`

`int_1^2(4x^3 - 3x^2 + 2x)dx = int_1^2(4x^3)dx - int_1^2 3x^2 dx + int_1^2 2x dx`

Evaluating each definite integral, using the formula `int x^n dx = (x^(n+1))/(n+1) + c` , yields:

`int_1^2(4x^3)dx = 4*(x^4)/4|_1^2 = 2^4 - 1^4 = 15`

`int_1^2 3x^2 dx =3x^3/3|_1^2 = 2^3 - 1^3 = 7`

`int_1^2 2x dx = 2x^2/2|_1^2 = 2^2 - 1^2 = 3`

Gathering the results, yields:

`int_1^2(4x^3 - 3x^2 + 2x)dx = 15 - 7 + 3 = 11`

Hence, evaluating the definite integral, using the fundamental theorem of calculus yields `int_1^2(4x^3 - 3x^2 + 2x)dx = 11.`