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 3 years ago
Evaluate the integral by interpreting it in terms of areas.
Integral ((1/2)x  (1))dx
 3 years ago
Evaluate the integral by interpreting it in terms of areas. Integral ((1/2)x  (1))dx

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patbatE21
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1321990987862:dw

slaaibak
 3 years ago
Best ResponseYou've already chosen the best response.0\[1/4 x^2  x\] 1/4* 3^2  3  (1/4 * 0^2  0) = 3/4

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0This is a triangle, so we want to look at it that way. Andras seems to have it.

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0two triangles, sorry

Andras
 3 years ago
Best ResponseYou've already chosen the best response.0The area that you need is the shaded one on my drawing. Above the x line it is + below it is . So you need to count 2 triangles

agreene
 3 years ago
Best ResponseYou've already chosen the best response.1Alternatively, you can split the integral and look at one triangle and one rectangle. \[\int\limits_{0}^{3} \frac13x1dx=\int\limits_{0}^{3}\frac{x}3dx\int\limits_{0}^{3}1dx\] graphing y=1/3x and y=1 then finding the limits, and remembering you need to subtract one: dw:1321993923933:dw You should find: y= 1/3 x from 0,3 to be 3/2 and y=3 from 0,3 to be 3 3/23 = 3/2
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