What is the integral from 1 to 5 of xsqrt(5x^2-4) ?

The integral from 1 to 5 of xsqrt(5x^2-4) is 266/3

Popular >

integral from 1 to 5 of xsqrt(5x^2-4)

\int_{1}^{5} x 5 x^{2} - 4 d x

\frac{266}{3}

Decimal

88.66666 \dots

Solution steps

\int_{1}^{5} x 5 x^{2} - 4 d x

Apply u-substitution

: \int_{1}^{121} \frac{u}{10} d u

= \int_{1}^{121} \frac{u}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{1}^{121} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{121}

= \frac{1}{10} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{121}

Compute the boundaries:

\frac{2660}{3}

= \frac{1}{10} \cdot \frac{2660}{3}

Simplify

= \frac{266}{3}

\int_{0}^{2 π} ∣ sin (x + 1) ∣ d x

\int_{0}^{\frac{π}{2}} sin (4 x) d x

\int_{0}^{\frac{π}{2}} f (sin (x)) d x

\int_{0}^{1} \frac{x}{1 - x} d x

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

What is the integral from 1 to 5 of xsqrt(5x^2-4) ?
The integral from 1 to 5 of xsqrt(5x^2-4) is 266/3