What is the integral from 0 to 3 of t/(sqrt(7+t^2)) ?

The integral from 0 to 3 of t/(sqrt(7+t^2)) is 4-sqrt(7)

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integral from 0 to 3 of t/(sqrt(7+t^2))

\int_{0}^{3} \frac{t}{7 + t ^{2}} d t

4 - 7

Decimal

1.35424 \dots

Solution steps

\int_{0}^{3} \frac{t}{7 + t ^{2}} d t

Apply u-substitution

: \int_{7}^{16} \frac{1}{2 u} d u

= \int_{7}^{16} \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{7}^{16} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{7}^{16}

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{7}^{16}

Apply radical rule:

a^{\frac{1}{n}} = n a

= \frac{1}{2} [2 u]_{7}^{16}

Compute the boundaries:

8 - 27

= \frac{1}{2} (8 - 27)

Simplify

= 4 - 7

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

\int_{2}^{2} 1 + x^{3} d x

\int_{1}^{8} 3 w d w

\int_{0}^{6} (2 x) - (x^{2} - 4 x) d x

\int_{0}^{1} 3 y d y

What is the integral from 0 to 3 of t/(sqrt(7+t^2)) ?
The integral from 0 to 3 of t/(sqrt(7+t^2)) is 4-sqrt(7)