What is the integral from 3 to 11 of sqrt(2x+3) ?

The integral from 3 to 11 of sqrt(2x+3) is 98/3

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integral from 3 to 11 of sqrt(2x+3)

\int_{3}^{11} 2 x + 3 d x

\frac{98}{3}

Decimal Notation

32.66666 \dots

Solution steps

\int_{3}^{11} 2 x + 3 d x

Apply u-substitution

: \int_{9}^{25} \frac{u}{2} d u

= \int_{9}^{25} \frac{u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{9}^{25} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

Compute the boundaries:

\frac{196}{3}

= \frac{1}{2} \cdot \frac{196}{3}

Simplify

= \frac{98}{3}

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

\int_{\frac{π}{4}}^{\frac{π}{3}} sec^{2} (x) d x

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

\int_{0}^{1} \frac{x ^{2}}{3 + x ^{3}} d x

\int_{x^{2}}^{4} 3 t d t

What is the integral from 3 to 11 of sqrt(2x+3) ?
The integral from 3 to 11 of sqrt(2x+3) is 98/3