# Evaluate the integrals for f(x) shown in the figure below...?

I mostly just want how to do a) explained to me. I tried to use A = 1/2 pi r^2 for the area and splitting the integral into a product of the int. of 3 from [0,2] and the int. of f(x) from [0,2], but no dice. What am I doing wrong here??? The multiplication of f(x) is really throwing me for a loop. Can I not just pull the 3 out of the integral and calculate the area using the normal formula?

a) Integral of 3*f(x) from [0, 2]

b) Integral of 3*f(x) from [0,6]

c) Integral of 2*f(x) from [1, 4]

d) Integral of abs(4*f(x)) from [1, 6]

Some (wrong) answers given:

-3pi(0.5)^2

-3/2pi(0.5)^2

I'm just guessing at this point.

### 1 Answer

- RealProLv 72 months agoFavorite Answer
I don't really think "from" [0, 2] makes sense in the English language. It should be from 0 to 2, or ON [0, 2].

You say you're integrating the 3 after pulling it out??? That's not right. Learn the rules of integration slowly and methodically.

int k * f(x) dx =

k * int f(x) dx

if k is a real number independent of x.

So calculate

1) Integral of f(x) on [0, 2]

2) Integral of f(x) on [0,6]

3) Integral of f(x) on [1, 4]

4) Integral of abs(f(x)) on [1, 6]

Of course,

1) is -pi/2

2) is -pi/2 + 2pi

3) is (1/2)(-pi/2) + (1/2)(2pi)

4) is (1/2)pi/2 + 2pi (absolute value positivizes all the y-coordinates)

Then multiply by 3, 3, 2, 4 in order to get a), b), c), d) respectively.

In d) I used the fact that abs(4f(x)) = 4 abs(f(x)) for any f(x).

As it turns out I just can't read... yes, bad things happen when you're trying to integrate while angry. Anyway, I tried just plain pulling the 3 out (NOT integrating it) first but the problem is that I'm an idiot who can't read graph scales... thanks!