integral properties

Question

Integral of (3f(x)+7) dx= 28 . it has a lower bound at 3 and upper at 4, find fxdx

Answer 1

If we are given the integral you mentioned, we can break that up into 2 pieces:

We can solve ₃∫⁴7dx because, we know the antiderivative of 7 is 7x so:

₃∫⁴7dx = 7x evaluated between 3 and 4 = 7(4) - 7(3) = 28 - 21 = 7

So now we can say

₃∫⁴3f(x)dx + 7 = 28 and subtracting 7 from both sides gets us:

₃∫⁴3f(x)dx = 21

We can also pull the constant "3" outside the integral making our equation:

3•₃∫⁴f(x)dx = 21

Now we can divide both sides by 3 to get:

₃∫⁴f(x)dx = 7

And, I THINK that is what you are asking for.