# Finding area given definite integral

1. Jul 14, 2014

### grace77

Question :
View attachment 71328

My question is how did the 2a and 2b come from??
Equations:
Area of trapezoid =(a+b/2)(h)
Attempt:
I know that the area of a trapezoid is (a+b/2)(h)
However why is there now a 2a and 2b in its place? Could it be related to the 2s function??

Last edited by a moderator: Jul 14, 2014
2. Jul 14, 2014

### FilupSmith

Hope this helps

ba 2s ds = [s2]ba
this then becomes (b2-a2)

its just integral laws

3. Jul 14, 2014

### SteamKing

Staff Emeritus
Beats me.

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4. Jul 14, 2014

### FilupSmith

I'm pretty sure the this is what you're looking for:
$$\int ^{b}_{a}2xdx=\left[ x^{2}\right] ^{b}_{a}=b^{2}-a^{2}$$

~| FilupSmith |~

5. Jul 14, 2014

### HallsofIvy

Staff Emeritus
I cannot see the attachment. If your trapezoid has parallel sides of length a and b and height h, its area is NOT (a+ b/2)h. It is (a+ b)h/2 or ((a+ b)/2)h.