What is the integral from 0 to 1 of xsqrt(33x^2+16) ?

The integral from 0 to 1 of xsqrt(33x^2+16) is 31/11

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integral from 0 to 1 of xsqrt(33x^2+16)

\int_{0}^{1} x 33 x^{2} + 16 d x

\frac{31}{11}

Decimal

2.81818 \dots

Solution steps

\int_{0}^{1} x 33 x^{2} + 16 d x

Apply u-substitution

= \int_{16}^{49} \frac{u}{66} d u

Take the constant out:

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

= \frac{1}{66} \cdot \int_{16}^{49} u d u

Apply the Power Rule

= \frac{1}{66} [\frac{2}{3} u^{\frac{3}{2}}]_{16}^{49}

Compute the boundaries:

186

= \frac{1}{66} \cdot 186

Simplify

= \frac{31}{11}

What is the integral from 0 to 1 of xsqrt(33x^2+16) ?
The integral from 0 to 1 of xsqrt(33x^2+16) is 31/11