Integration of this... Watch

stephaimee
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I'm struggling to integrate this equation: V= 5+0.8(t-20)^2I'm not sure which element I should integrate first... I know how to integrate its just I don't know wether to multiply the brackets out FIRST by 0.8 and ^2 THEN integrate or integrate each element individually. So 0.8 then t then 20... I'm just not sure!Help us MUCH appreciated! Thanks!
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mik1a
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You can't integrate the "t" and then the "-20" separately because they are squared in the expression, and that will be different from just "t-20". Multiply out then integrate.

Integration is a linear operator, so integral of (t - 20) is equal to: integral of (t) plus integral of (-20). But any nonlinear operations such as the ()^2 must be done before integration. In other words, integral of (t-20)^2 is not equal to (integral of (t-20))^2.
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stephaimee
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(Original post by mik1a)
You can't integrate the "t" and then the "-20" separately because they are squared in the expression, and that will be different from just "t-20". Multiply out then integrate.

Integration is a linear operator, so integral of (t - 20) is equal to: integral of (t) plus integral of (-20). But any nonlinear operations such as the ()^2 must be done before integration. In other words, integral of (t-20)^2 is not equal to (integral of (t-20))^2.
So I have to expand the brackets to get the quadratic, then expand by 0.8 then integrate each expression?
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mik1a
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You definitely have to expand the brackets. You don't need to expand the 0.8 because that's just a constant. I guess a simpler example would be "integrate 2x". You would treat that as x+x and obtain x^2/2 + x^2/2 as your answer, or you could integrate the whole thing and carry the 2, and get x^2. The same applies to the factor of 0.8.
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