What is the integral from 0 to 3 of tsqrt(1+t^2) ?

The integral from 0 to 3 of tsqrt(1+t^2) is (10sqrt(10)-1)/3

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integral from 0 to 3 of tsqrt(1+t^2)

\int_{0}^{3} t 1 + t^{2} d t

\frac{10 10 - 1}{3}

Decimal

10.20759 \dots

Solution steps

\int_{0}^{3} t 1 + t^{2} d t

Apply u-substitution

: \int_{1}^{10} u^{2} d u

= \int_{1}^{10} u^{2} d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{10 10}{3} - \frac{1}{3}

= \frac{10 10}{3} - \frac{1}{3}

Simplify

= \frac{10 10 - 1}{3}

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What is the integral from 0 to 3 of tsqrt(1+t^2) ?
The integral from 0 to 3 of tsqrt(1+t^2) is (10sqrt(10)-1)/3