for the first one it would be helpful for you to draw the graph of x^2 and the see what areas you are calculating, hopefully it will become clearer to you.
1) explain geometrically why the integral from 1 to 2 of x^2 dx equals the integral from 0 to 2 of x^2 dx minus the integral from 0 to 1 of x^2 dx and show that can be writen as the integral from 1 to 2 of x^2 dx = the integral from 1 to 0 of x^2 dx + the integral from 0 to 2 of x^2 dx
AND...
2) find a E (0, 2pi] such that the integral from 0 to a of sin x dx = 0
THANKS FOR THE HELP!!!
You can either solve for by first integrating and then solving the resulting trigonometric equation.
Or you can draw a graph of starting at (0, 0) and ending at (2 pi, 0) and examine it to see what value of x gives a graph with the same area above the x-axis as below (use symmetry). That value of x will be the value of you require.
For Q2) it looks like you're expected to know what the integral of sin x is. Have you been taught that?
http://www.ucl.ac.uk/Mathematics/geo...tnb/int2a.html
Table of Integrals