A = integral, from 0 to 2, of (x + 6) - x^2 dx

Limits, differentiation, related rates, integration, trig integrals, etc.
stripling_warrior
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A = integral, from 0 to 2, of (x + 6) - x^2 dx

I have no clue!!!

$A=\int_0^2[(x+6)-x^2]dx$

stapel_eliz
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stripling_warrior wrote:$A=\int_0^2[(x+6)-x^2]dx$

Use what you learned back in algebra to expand the polynomial integrand.

Then apply the Power Rule in reverse.

Evaluate the result at x = 2 and at x = 0.

Subtract to obtain the integral value.

If you get stuck, please reply showing how far you have gotten.

Thank you!

stripling_warrior
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Joined: Wed May 06, 2009 7:42 pm
Location: California!!!
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Re: A = integral, from 0 to 2, of (x + 6) - x^2 dx

Thanks!!!!

$=\left[\frac{x^2}{2}+6x-\frac{{x^3}}{3}\right]_0^2= \frac{34}{3}-0= \frac{34}{3}$