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

The integral from-4 to-1 of x^2(3-4x) is 318

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integral from-4 to-1 of x^2(3-4x)

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

318

Solution steps

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

Expand

x^{2} (3 - 4 x) : 3 x^{2} - 4 x^{3}

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

\int_{- 4}^{- 1} 3 x^{2} d x = 63

\int_{- 4}^{- 1} 4 x^{3} d x = - 255

= 63 - (- 255)

Simplify

= 318

\int_{0}^{1} (- x^{3} - 2 x^{2} + 3 x) d x

\int_{1}^{3 x} (x^{3} e^{x y}) d y

\int_{1}^{4} 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

\int_{x}^{x^{3}} e^{t^{2}} d t

\int_{0}^{2} 4 - y^{2} d y

What is the integral from-4 to-1 of x^2(3-4x) ?
The integral from-4 to-1 of x^2(3-4x) is 318