find distance using an integral that cuts the x-axis, without adding parts?

Question

if the equation is 9-t^2, you could add the integrals from 0-3 and 3-6, but i want to do it in one step. on the calculator, you can do nDeriv(abs(9-x^2),x,0,6) and you get the right answer because the absolute value brings the negative curve above the axis. but to do this by hand, evaluating 9t-(t^3)/3 from 0 to 6 gives the wrong answer. changing the - to a plus is also wrong. how can i do this by hand and get the correct 54 as an answer?

Update:

i meant the math9 thing, i just said nDeriv cuz it was on my mind... yeah intergral. but i want to do it by hand, not on the calc. how can i do this

sunset8949 · Accepted Answer

On the calculator, (At least, on the TI-83 Plus that I have) you click "MATH" then click the number 9, which should give you something that says "fnInt( " So, you type in:

fnInt(9-x^2 , x , 0, 6) and it should work....

The nDeriv( Finds the derivative at a point.

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find distance using an integral that cuts the x-axis, without adding parts?

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