Question

how to integrate plzz z help​

Answer 1

Answer:

First, I would tell you the formulas needed for this question:

• Integral f(x) + g(x) = Integral f(x) + Integral g(x)

This means that the sign of integral can be applied separately to two functions. In this example, ax^2 + bx are the two terms. So, we can integrate them separately.

• Integral x^n dx = x^(n+1)/n+1

Now, let's solve the question.

Solution:

Integral x(ax + b) dx = Integral (ax^2 +bx) dx

integral ax^2 dx + Integral bx dx

a × integral x^2 dx + b × integral x dx

(a, b being constant are taken out)

(ax^3)/3 + (bx^2)/2

Putting the limits,

(aL^3)/3 - a(0)^3/3 + (bL^2)/2 + b(0)^2/2

(aL^3)/3 + (bL^2)/2

(2aL^3 + 3bL^2)/6

This is the answer.