What is the integral from 3 to 4 of (3+2y)^2 ?

The integral from 3 to 4 of (3+2y)^2 is 301/3

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integral from 3 to 4 of (3+2y)^2

\int_{3}^{4} (3 + 2 y)^{2} d y

\frac{301}{3}

Decimal

100.33333 \dots

Solution steps

\int_{3}^{4} (3 + 2 y)^{2} d y

Expand

(3 + 2 y)^{2} : 9 + 12 y + 4 y^{2}

= \int_{3}^{4} 9 + 12 y + 4 y^{2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{3}^{4} 9 d y + \int_{3}^{4} 12 y d y + \int_{3}^{4} 4 y^{2} d y

\int_{3}^{4} 9 d y = 9

\int_{3}^{4} 12 y d y = 42

\int_{3}^{4} 4 y^{2} d y = \frac{148}{3}

= 9 + 42 + \frac{148}{3}

Simplify

9 + 42 + \frac{148}{3} : \frac{301}{3}

= \frac{301}{3}

What is the integral from 3 to 4 of (3+2y)^2 ?
The integral from 3 to 4 of (3+2y)^2 is 301/3