What is the integral from 0 to 1 of (4x^3-21x^2) ?

The integral from 0 to 1 of (4x^3-21x^2) is -6

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integral from 0 to 1 of (4x^3-21x^2)

\int_{0}^{1} (4 x^{3} - 21 x^{2}) d x

- 6

Solution steps

\int_{0}^{1} 4 x^{3} - 21 x^{2} 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_{0}^{1} 4 x^{3} d x - \int_{0}^{1} 21 x^{2} d x

\int_{0}^{1} 4 x^{3} d x = 1

\int_{0}^{1} 21 x^{2} d x = 7

= 1 - 7

Simplify

= - 6

\int_{0}^{1} \frac{x + 1}{x ^{3} - 1} d x

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\int_{1}^{2} [\frac{I n x}{x ^{2}}] d x

\int_{0}^{1} \frac{1}{x + y} d y

\int_{\frac{π}{4}}^{\frac{π}{2}} - 2 x csc^{2} (x) d x

What is the integral from 0 to 1 of (4x^3-21x^2) ?
The integral from 0 to 1 of (4x^3-21x^2) is -6