trouble with few cal questions

College Majors Engineering Majors
1

<p>help would be greatly appreciated.</p>

<p>A) find areas of the regions bounded by f(x) = x^2 and g(x) = (x^2/2) +2</p>

<p>B) find areas of the regions bounded by f(x) = x^2 and g(x) = (1 - x^2)</p>

<p>C) area of graph of f(x) = sqrt(x), the horizontal axis, and the vertical axis through (2,0)</p>

<p>lastly, i have no idea how to approach</p>

<p>Prove that int(x^3dx) from 0 to b = (b^4/4), by considering partitions into n equal subintervals, using the forumula for summation i=1 to n of i^3.</p>

<p>help would be greatly appreciated</p>

2

<p>hint:
to find area bounded by 2 functions, you are finding the area under the greater function - the area under the lesser function</p>

3

<p>how would i prove the last question without the fundamental theorem of calculus?</p>

4

<p>I am not sure if I really understand what you are asking with the last question. If I do understand, you should find the limit as n-> oo of a Riemann sum with n subdivisions</p>