Question

If f(x)=
`\int\limits^x_0` cos(t^2)dt for -2.5≤x≤2.5, on which interval is f increasing?

Answer 1

[-2.5, 2.17) U (-1.25, 1.25) U (2.17, 2.5]

Explanation:

Function is increasing when

f'(x) > 0

f'(x) = cos(x²)

cos(x²) > 0

When x² is:

0《x² < pi/2

3pi/2 < x²《2.5²

0《x² < 1.570796327

-1.253314137 < x < 1.253314137

4.71238898 < x²《6.25

-2.5《x < 2.170803764

2.170803764 < x《2.5