What is the integral from 0 to 1 of x^3sqrt(1+9x^4) ?

The integral from 0 to 1 of x^3sqrt(1+9x^4) is (10sqrt(10)-1)/(54)

Popular >

integral from 0 to 1 of x^3sqrt(1+9x^4)

\int_{0}^{1} x^{3} 1 + 9 x^{4} d x

\frac{10 10 - 1}{54}

Decimal

0.56708 \dots

Solution steps

\int_{0}^{1} x^{3} 1 + 9 x^{4} d x

Apply u-substitution

: \int_{1}^{10} \frac{u}{36} d u

= \int_{1}^{10} \frac{u}{36} d u

Take the constant out:

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

= \frac{1}{36} \cdot \int_{1}^{10} u d u

Apply the Power Rule

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

= \frac{1}{36} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{10}

Compute the boundaries:

\frac{20 10}{3} - \frac{2}{3}

= \frac{1}{36} (\frac{20 10}{3} - \frac{2}{3})

Simplify

= \frac{10 10 - 1}{54}

\int_{0}^{2} x^{2} (2 x - x) d x

\int_{0}^{1} (x^{2} + 6) d x

\int_{- 5 π}^{6 π} cos^{2} (x) d x

\int_{0}^{2} - x^{2} + 4 d x

\int_{0}^{7} 3 x + 9 d x

What is the integral from 0 to 1 of x^3sqrt(1+9x^4) ?
The integral from 0 to 1 of x^3sqrt(1+9x^4) is (10sqrt(10)-1)/(54)