Question

F of x equals the integral from 0 to x of the cosine of t squared . Use your calculator to find f '(1).

1. 0.709
2. 0.292
3. 0.842
4. 0.540

Answer 1

First, if we have a function defined as:

`G(x) = \int\limits^x_0 {f(t)} \, dt`

then:

G'(x) = f(x)

`F(x) = \int\limits^x_0 {cos(t)^2} \, dt`

then:

F' = dF/dt = cos(t)^2

F'(1) = cos(1)^2 = 0.2919

If we round it up to the third digit after the decimal point we get:

F'(1) = 0.292

The correct option is the second one.