What is the integral from 0 to 1 of (5x^4-4x^3) ?

The integral from 0 to 1 of (5x^4-4x^3) is 0

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integral from 0 to 1 of (5x^4-4x^3)

\int_{0}^{1} (5 x^{4} - 4 x^{3}) d x

0

Solution steps

\int_{0}^{1} 5 x^{4} - 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_{0}^{1} 5 x^{4} d x - \int_{0}^{1} 4 x^{3} d x

\int_{0}^{1} 5 x^{4} d x = 1

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

= 1 - 1

Simplify

= 0

g (x) = 2 x^{2}

h \to 0 lim (\frac{cos ( h )}{h})

\int \frac{3 x}{9 + x ^{2}} d x

f (x) = 2^{2 x}

\int_{1}^{5} 2 r^{2} ln (r) d r

What is the integral from 0 to 1 of (5x^4-4x^3) ?
The integral from 0 to 1 of (5x^4-4x^3) is 0