What is the integral from 0 to 3 of 2y ?

The integral from 0 to 3 of 2y is 9

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integral from 0 to 3 of 2y

\int_{0}^{3} 2 y d y

9

Solution steps

\int_{0}^{3} 2 y d y

Take the constant out:

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

= 2 \cdot \int_{0}^{3} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{3}

= 2 [\frac{y ^{2}}{2}]_{0}^{3}

Compute the boundaries:

\frac{9}{2}

= 2 \cdot \frac{9}{2}

Simplify

= 9

\int_{1}^{x^{3}} \frac{g ( t )}{4 + t ^{2}} d t

\int_{1}^{7} (1 - x) (x - 7) d x

\int_{0}^{2} \frac{1}{4 x + 1} d x

\int_{2}^{3} \frac{1}{( x - 1 ) ^{2}} d x

\int_{3}^{7} \frac{3}{7 - x} d x