No, there is not a product rule for integration.
To integrate (2x - 1)(6x + 5), start expanding the product:
(2x - 1)(6x + 5) = 12x^2 + 10x - 6x - 5 = 12x^2 + 4x - 5.
Now, I guess you know how to integrate that:
∫ (12x^2 + 4x - 5) dx = ∫12x^2 dx + ∫4x dx + ∫ (-5) dx = 4x^3 + 2x^2 - 5x + C
Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
Assume Charles charges $7*3=$21 if he babysits for 2,5 hours (that is 2 and a half hours).
That is we are not considering Charles babysitting exactly 1, 2, 3 or 4 hours, but also in between times.
then we can write the following piecewise function to describe the situation:
f is a function from (0, 4] to {$7, $14, $21, $28}