# Thread: Help with these 2 calc probs

1. ## Help with these 2 calc probs

I need help with my calculus homework. i got these two problems to solve but i don't understand how to solve them. any ideas?
Question 1:

Question 2

2. Originally Posted by koolbklyn
I need help with my calculus homework. i got these two problems to solve but i don't understand how to solve them. any ideas?
Question 1:

Fundamental theorem of calculus: If F(x) is an anti-derivative of f(x) such that F(a)= 0 then
$\displaystyle \int_a^x f(t)dt= F(x)$

Question 2
For a function whose graph is always above the x-axis, the integral can be thought of as "area under the curve". The thing to be careful about with this problem is that part of the graph is below the x-axis. That area has to be thought of as "negative area".

Since each of the vertical lines represents a step of 1/2, from x=0 to x= 1, the graph is below the x-axis. The area is that of a right triangle with base 1 and height 1. That area will be negative (if you like, think of it as a triangle with base 1 and height -1).

For x from 1 to 6, the graph is above the x-axis and the area is that of a trapezoid with height 1 and bases of length 5 and 3.

For x from 6 to 7, the graph is again below the x-axis the area is exactly the same as the first triangle.

Use geometric area formulas to find those areas.

3. thanks. i understood how to solve question 2 but i'm still confused on your to solve question 1. is it possible for you to show me how to solve it step by step?