What is the integral from 1 to 12 of 2x ?

The integral from 1 to 12 of 2x is 143

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integral from 1 to 12 of 2x

\int_{1}^{12} 2 x d x

143

Solution steps

\int_{1}^{12} 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}^{12} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{1}^{12}

= 2 [\frac{x ^{2}}{2}]_{1}^{12}

Compute the boundaries:

\frac{143}{2}

= 2 \cdot \frac{143}{2}

Simplify

= 143

\int \frac{9 e ^{2 t}}{1 + e ^{4 t}} d t

f (x) = \frac{1}{2} x^{2} + 7 x

\int co tan (x) d x

x \to \frac{π}{3} lim (x cos (x))

y^{^{'}} + 2 y = e^{2 x}

What is the integral from 1 to 12 of 2x ?
The integral from 1 to 12 of 2x is 143