If F is an antiderivative of the function f and f(0) = 25, estimate F(7)

The function f is = Integral from 0 to 7 of f(x)dx

Question

If F is an antiderivative of the function f and f(0) = 25, estimate F(7)

The function f is = Integral from 0 to 7 of f(x)dx

anonymous · Answer

$$f=\int_{0}^{7}f(x)dx$$$$f'=F(7)$$
$$F'(a)\Delta x\approx F(a+\Delta x)-F(a) $$
$$f(0)7\approx F(7)-F(0) $$
$$F(7)\approx f(0)7+F(0) $$
$$F(7)\approx 25*7-25 \approx 150$$
In the last step, -25 is obtained by switching the signs on the integral.

This is probably wrong btw.

anonymous · Answer

*switching the intervals, which leads to the multiplication by -1