definite integrals

Question

let G'(t)= g(t) and G(0)=4. Use the figure to find the values of G(t) at t=5,10, 20, 25.

there is a graph provided of the function g(t). but how do find the values of g(t)?

Answer 1

If G'(t) = g(t) then G(t) = ∫g(t) dt and the integral is the area under the curve.

I'm assuming that the graph is g(t). To find G(t), find the area under the curve of g(t). You can typically use geometry to find the are under the graph of straight line segments. Use the initial information that G(0) = 4 so whatever area you get from 0 to 5, you would add 4 to it, whatever area you get from 0 to 10, add 4 to it, etc.