# Thread: integral help

1. ## integral help

so i was working with an integral and I have something like this

$\frac{x^2}{1+x^4} \int_{2}^{\sin{x}} dt + \frac{1}{1+x^4} \int_{2}^{\sin{x}} \cos{t^7} dt$

my question is does $\int_{2}^{\sin{x}} dt$ = 0? because its like taking the area under the curve of nothing?

2. It is the same as

$
\frac{x^2}{1+x^4} \int_{2}^{\sin{x}} \; 1 \; dt
$

$
\int \; f(x) \; dx \;= \int \; 1 \; dx.
$

It is the area under function f(x)=1.

3. wow that entirely makes more sense. thanks

4. Originally Posted by zzzoak
It is the same as

$
\frac{x^2}{1+x^4} \int_{2}^{\sin{x}} \; 1 \; dt
$

$
\int \; f(x) \; dx \;= \int \; 1 \; dx.
$

It is the area under function f(x)=1.
I am just curious on this one. The integral becomes

$\int_{2}^{\sin{x}} dt=|Sin x -2|$

Is this right?

5. why modulus?

6. Originally Posted by BAdhi
why modulus?
Sorry, that shouldnt be there.

Just Sinx -2.

So IM guessing thats right.