What is the integral from-1 to 2 of 3xsqrt(3x^2+2) ?

The integral from-1 to 2 of 3xsqrt(3x^2+2) is (14sqrt(14)-5sqrt(5))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 2 of 3xsqrt(3x^2+2)

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

\frac{14 14 - 5 5}{3}

Decimal Notation

13.73428 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{5}^{14} \frac{u}{6} d u

= 3 \cdot \int_{5}^{14} \frac{u}{6} d u

Take the constant out:

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

= 3 \cdot \frac{1}{6} \cdot \int_{5}^{14} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{14}

= 3 \cdot \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{14}

Simplify

3 \cdot \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{14} : \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{14}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{14}

Compute the boundaries:

\frac{28 14 - 10 5}{3}

= \frac{1}{2} \cdot \frac{28 14 - 10 5}{3}

Simplify

= \frac{14 14 - 5 5}{3}

\int 10 d x

x \to 2 + lim (x)

\int \frac{21}{1 - cos ( 7 x )} d x

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) !}

y^{^{''}} + 2 y^{^{'}} - y = 0

What is the integral from-1 to 2 of 3xsqrt(3x^2+2) ?
The integral from-1 to 2 of 3xsqrt(3x^2+2) is (14sqrt(14)-5sqrt(5))/3