# Math Help - Interval of Decrease

1. ## Interval of Decrease

Let g be the function given by $g(x) = \int_{0}^{x}sin(t^2)dt$ for -1 < x < 3. On which interval is g decreasing?

2. Originally Posted by xxlvh
Let g be the function given by $g(x) = \int_{0}^{x}sin(t^2)dt$ for -1 < x < 3. On which interval is g decreasing?
Notice that $g'(x) = \sin (x^2)$.
Now you need to find $g'>0$?

3. Ok, I solved it by graphing and the solution I had was approximately 1.772 < x < 2.507

4. Originally Posted by xxlvh
Ok, I solved it by graphing and the solution I had was approximately 1.772 < x < 2.507
Do you see how you get the number?

Hint: $\sin (y) > 0$ for what $y$?
Now set $y=x^2$ and solve for $x$.