What is the integral from 0 to 1 of 7xsqrt(x^2+9) ?

The integral from 0 to 1 of 7xsqrt(x^2+9) is 7((10sqrt(10))/3-9)

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integral from 0 to 1 of 7xsqrt(x^2+9)

\int_{0}^{1} 7 x x^{2} + 9 d x

7 (\frac{10 10}{3} - 9)

Decimal Notation

10.78647 \dots

Solution steps

\int_{0}^{1} 7 x x^{2} + 9 d x

Take the constant out:

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

= 7 \cdot \int_{0}^{1} x x^{2} + 9 d x

Apply u-substitution

: \int_{3}^{10} u^{2} d u

= 7 \cdot \int_{3}^{10} u^{2} d u

Apply the Power Rule

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

= 7 [\frac{u ^{3}}{3}]_{3}^{10}

Compute the boundaries:

\frac{10 10}{3} - 9

= 7 (\frac{10 10}{3} - 9)

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What is the integral from 0 to 1 of 7xsqrt(x^2+9) ?
The integral from 0 to 1 of 7xsqrt(x^2+9) is 7((10sqrt(10))/3-9)