What is the integral from 0 to pi of 3x^2+cos(x) ?

The integral from 0 to pi of 3x^2+cos(x) is pi^3

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integral from 0 to pi of 3x^2+cos(x)

\int_{0}^{π} 3 x^{2} + cos (x) d x

π^{3}

Decimal

31.00627 \dots

Solution steps

\int_{0}^{π} 3 x^{2} + cos (x) 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}^{π} 3 x^{2} d x + \int_{0}^{π} cos (x) d x

\int_{0}^{π} 3 x^{2} d x = π^{3}

\int_{0}^{π} cos (x) d x = 0

= π^{3} + 0

Simplify

= π^{3}

\frac{x}{x ^{- 1} + 12}

\frac{d}{d x} (\frac{- x ^{2} + 1}{( x ^{2} + 1 ) ^{2}})

\frac{\partial}{\partial x} (e^{- x} \cdot y)

arcsec (2 x)

\int \frac{x + 2}{x ^{2} - 2 x - 15} d x

What is the integral from 0 to pi of 3x^2+cos(x) ?
The integral from 0 to pi of 3x^2+cos(x) is pi^3