What is the integral from 0 to 1 of xsqrt(24x^2+25) ?

The integral from 0 to 1 of xsqrt(24x^2+25) is 109/36

Popular >

integral from 0 to 1 of xsqrt(24x^2+25)

\int_{0}^{1} x 24 x^{2} + 25 d x

\frac{109}{36}

Decimal

3.02777 \dots

Solution steps

\int_{0}^{1} x 24 x^{2} + 25 d x

Apply u-substitution

: \int_{25}^{49} \frac{u}{48} d u

= \int_{25}^{49} \frac{u}{48} d u

Take the constant out:

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

= \frac{1}{48} \cdot \int_{25}^{49} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{25}^{49}

= \frac{1}{48} [\frac{2}{3} u^{\frac{3}{2}}]_{25}^{49}

Compute the boundaries:

\frac{436}{3}

= \frac{1}{48} \cdot \frac{436}{3}

Simplify

= \frac{109}{36}

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

\int_{1}^{7} \frac{3}{x} d x

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

\int_{π}^{l n (x)} cos (e^{t}) d t

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

What is the integral from 0 to 1 of xsqrt(24x^2+25) ?
The integral from 0 to 1 of xsqrt(24x^2+25) is 109/36