What is the integral from-1 to 3 of 2x ?

The integral from-1 to 3 of 2x is 8

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integral from-1 to 3 of 2x

\int_{- 1}^{3} 2 x d x

8

Solution steps

\int_{- 1}^{3} 2 x d x

Take the constant out:

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

= 2 \cdot \int_{- 1}^{3} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 1}^{3}

= 2 [\frac{x ^{2}}{2}]_{- 1}^{3}

Compute the boundaries:

4

= 2 \cdot 4

Simplify

= 8

\int_{1}^{\infty} \frac{1}{ln ( x )} d x

\int_{0}^{x} 2 z e^{- x^{2}} d y

\int_{0}^{4} - 2 x^{2} + 8 x d x

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

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