What is the integral from 1 to 2 of 4x^3-3x^2+2x ?

The integral from 1 to 2 of 4x^3-3x^2+2x is 11

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integral from 1 to 2 of 4x^3-3x^2+2x

\int_{1}^{2} 4 x^{3} - 3 x^{2} + 2 x d x

11

Solution steps

\int_{1}^{2} 4 x^{3} - 3 x^{2} + 2 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} 4 x^{3} d x - \int_{1}^{2} 3 x^{2} d x + \int_{1}^{2} 2 x d x

\int_{1}^{2} 4 x^{3} d x = 15

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 2 x d x = 3

= 15 - 7 + 3

Simplify

= 11

\int_{0}^{1} 2 e^{\frac{x}{7}} + 5 d x

\int_{0}^{t} sin (x) \cdot sin (t - x) d x

\int_{0}^{4} x 25 - x^{2} d x

\int_{x}^{1} (x + y) d y

\int_{3}^{5} 25 - x^{2} d x

What is the integral from 1 to 2 of 4x^3-3x^2+2x ?
The integral from 1 to 2 of 4x^3-3x^2+2x is 11