What is the integral from 0 to 2 of 3e^{2x}-4x ?

The integral from 0 to 2 of 3e^{2x}-4x is (3(e^4-1))/2-8

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integral from 0 to 2 of 3e^{2x}-4x

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

\frac{3 ( e ^{4} - 1 )}{2} - 8

Decimal

72.39722 \dots

Solution steps

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

\int_{0}^{2} 3 e^{2 x} d x = \frac{3 ( e ^{4} - 1 )}{2}

\int_{0}^{2} 4 x d x = 8

= \frac{3 ( e ^{4} - 1 )}{2} - 8

What is the integral from 0 to 2 of 3e^{2x}-4x ?
The integral from 0 to 2 of 3e^{2x}-4x is (3(e^4-1))/2-8