What is the integral from-1 to 4 of (5x^4-8x^3+6) ?

The integral from-1 to 4 of (5x^4-8x^3+6) is 545

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integral from-1 to 4 of (5x^4-8x^3+6)

\int_{- 1}^{4} (5 x^{4} - 8 x^{3} + 6) d x

545

Solution steps

\int_{- 1}^{4} 5 x^{4} - 8 x^{3} + 6 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}^{4} 5 x^{4} d x - \int_{- 1}^{4} 8 x^{3} d x + \int_{- 1}^{4} 6 d x

\int_{- 1}^{4} 5 x^{4} d x = 1025

\int_{- 1}^{4} 8 x^{3} d x = 510

\int_{- 1}^{4} 6 d x = 30

= 1025 - 510 + 30

Simplify

= 545

f^{^{'}} (x) = e^{x}

\int - 6 x e^{x} d x

\int \frac{e ^{x} ( e ^{x} + 1 )}{( e ^{x} - 1 ) ^{3}} d x

\frac{d y}{d x} = 3 (2 - y)

\frac{d y}{d x} = \frac{x y + y ^{2}}{x ^{2}}

What is the integral from-1 to 4 of (5x^4-8x^3+6) ?
The integral from-1 to 4 of (5x^4-8x^3+6) is 545