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

The integral from-2 to 4 of (3x^2-4x+5) is 78

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

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

78

Solution steps

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

\int_{- 2}^{4} 3 x^{2} d x = 72

\int_{- 2}^{4} 4 x d x = 24

\int_{- 2}^{4} 5 d x = 30

= 72 - 24 + 30

Simplify

= 78

\int_{- 6}^{6} 6 - ∣ x ∣ d x

\int_{0}^{2} 4^{3 x} d x

\int_{x}^{1} 6 x d x

\int_{0}^{1} \frac{1}{x ^{q}} d x

What is the integral from-2 to 4 of (3x^2-4x+5) ?
The integral from-2 to 4 of (3x^2-4x+5) is 78