What is the integral from-1 to 2 of 4x ?

The integral from-1 to 2 of 4x is 6

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integral from-1 to 2 of 4x

\int_{- 1}^{2} 4 x d x

6

Solution steps

\int_{- 1}^{2} 4 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{- 1}^{2} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 1}^{2}

= 4 [\frac{x ^{2}}{2}]_{- 1}^{2}

Compute the boundaries:

\frac{3}{2}

= 4 \cdot \frac{3}{2}

Simplify

= 6

\int_{1}^{2} 1 + x e^{x} d x

\int_{- 1}^{1} (2 - 2 x^{2}) d x

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\int_{0}^{2} \frac{t}{5 + t ^{2}} d t