0
$\begingroup$

I just started doing integration and I dont know what the curly bracket(f(x)= 4 for x<4 etc...) means:enter image description here

  • 3
    The more interesting problem (for me at least) which platform was this question from? – 2017-01-13
  • 2
    @Chinny84 looks like WebAssign to me. – 2017-01-13

2 Answers 2

2

Note that $\int_a^b f(x) dx = \int_a^c f(x) dx + \int_c^b f(x) dx$. IN this case, take $a=0$, $b = 8$ and $c=4$. And then use the appropriate part of definition of $f(x)$ on each interval -- between $0$ and $4$ it is $4$, and between $4$ and $8$ it is $x$.

So, the integral is $\int_0^4 4 dx + \int_4^8 x dx$.

  • 0
    What is the answer? I got 20 but it is wrong. Any idea? I used the property of the integrals for the constant term..4(4-0) + 8-4 = 20 – 2017-01-13
  • 1
    @Chris your computation of second integral is false. The antiderivative of $x$ is not $x$. – 2017-01-13
5

I dont know what the curly bracket(f(x)= 4 for x<4 etc...) means

That's called a piecewise function, because it's defined in pieces. It's typically prerequisite knowledge for calculus, so definitely make sure you understand it before moving too much farther.

The piecewise function you provided says:

$$ \text{If $x < 4$ then the value of $f(x)$ is $4$.} $$ $$ \text{If $x \ge 4$ then the value of $f(x)$ is $x$.} $$ For example, $f(2) = 4$ because $2 < 4$ and $f(12) = 12$ because $12 \ge 4$.

So to integrate it, split up the integral at $x=4$ as explained in Batman's answer.