100 Points!

Please provide steps.
Solve number 56.

2

Step-by-step explanation:

∫₀⁴ p / √(9 + p²) dp

If u = 9 + p², then du = 2p dp.  So ½ du = p dp.

When p = 0, u = 9.  When p = 4, u = 25.

∫₉²⁵ (½ du) / √u

½ ∫₉²⁵ u^-½ du

½ (2u^½) |₉²⁵

√u |₉²⁵

√25 − √9

5 − 3

2

2

Step-by-step explanation:

We will use a u substitution

Let u = 9+p^2

du = 2p dp

The lower limit becomes

u = 9+0^2 = 9

The upper limit becomes

u = 9+4^2 = 25

   where a is 25

We know the intergral of 1 / sqrt(u)  is  sqrt(u)/ 1/2

1/2 * sqrt(u)/(1/2) evaluated at 25 and 9

sqrt(u)  where u is25 - sqrt(u)  where u is 9

sqrt(25) - sqrt(9)

5-3

2

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w