What is the integral from 0 to 3 of 4tsqrt(t^2+1) ?

The integral from 0 to 3 of 4tsqrt(t^2+1) is (4(10sqrt(10)-1))/3

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integral from 0 to 3 of 4tsqrt(t^2+1)

\int_{0}^{3} 4 t t^{2} + 1 d t

\frac{4 ( 10 10 - 1 )}{3}

Decimal

40.83036 \dots

Solution steps

\int_{0}^{3} 4 t t^{2} + 1 d t

Take the constant out:

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

= 4 \cdot \int_{0}^{3} t t^{2} + 1 d t

Apply u-substitution

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

= 4 \cdot \int_{1}^{10} u^{2} d u

Apply the Power Rule

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

= 4 [\frac{u ^{3}}{3}]_{1}^{10}

Compute the boundaries:

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

= 4 (\frac{10 10}{3} - \frac{1}{3})

Simplify

= \frac{4 ( 10 10 - 1 )}{3}

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What is the integral from 0 to 3 of 4tsqrt(t^2+1) ?
The integral from 0 to 3 of 4tsqrt(t^2+1) is (4(10sqrt(10)-1))/3