What is the integral from 0 to 1 of (5x^4-3x^2+1) ?

The integral from 0 to 1 of (5x^4-3x^2+1) is 1

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integral from 0 to 1 of (5x^4-3x^2+1)

\int_{0}^{1} (5 x^{4} - 3 x^{2} + 1) d x

1

Solution steps

\int_{0}^{1} 5 x^{4} - 3 x^{2} + 1 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} 3 x^{2} d x + \int_{0}^{1} 1 d x

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

\int_{0}^{1} 3 x^{2} d x = 1

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

= 1 - 1 + 1

Simplify

= 1

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

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\int_{1}^{5} cos (x) d x

\int_{1}^{9} (\frac{2}{x}) d x

\int_{π}^{x} cos (2 x) d x

What is the integral from 0 to 1 of (5x^4-3x^2+1) ?
The integral from 0 to 1 of (5x^4-3x^2+1) is 1