<p>The question is:
Let f(x)=3 if x is less than or equal to 3 and 6-x if x is greater than 3. Use geometric formulas to finmd the integration from 0 to 5 f(x)dx.</p>
<p>I would sketch a graph of this particular function. Draw line segments from the x-axis up to f(x) = 3 at x = 0 and x = 3, and draw line segments from the x-axis up to f(x) = 6-x at x = 3 and x = 5.</p>
<p>You should recognize the two shapes that are enclosed and can find the areas of those pieces.</p>
<p>BTW, what text are you doing that you guys are doing integration at this time of the year?</p>
<p>This one is just finding the area underneath the curve from x=0 to 5, which is easy to do since you have a rectangle and a triangle as the curve</p>
<p>We're not doing this yet in the year. I took calc 1 over the summer and had a really bad teacher and I was just going through my old notes and tests looking at questions i couldn't answer before. I'm taking AP Calc AB (my school won't allow me to move up even though I took calc 1 at a CC) and we use the same book I used over the summer.</p>
<p>Very easy - do the integral of 3 from 0 to 3 - which is 9.</p>
<p>Then do the integral of 6-x from 3 to 5 = 6x-.5x^2 from 3 to 5 = 27.5 - 13.5 = 14.</p>
<p>Add them up to get 14 + 9 = 23. :)</p>
<p>sishu, the question asked for geometric formulas, which your integral of 6-x omits.</p>