Area Between Two Curves Integral

Question

Which of the following is an example of finding the area between the curves $$f(x)=5*x-x^2$$ and $$g(x)=x$$ on the interval from x = 0 to x = 4?

Accepted Answer

Calculating $$\int_0^4 \left[(5*x-x^2)-x\right]\,dx$$ to determine the area between the curves.

Answer

Calculating $$\int_0^4 \frac{5*x-x^2}{x}\,dx$$ which incorrectly introduces division by x.

Answer

Calculating $$\int_0^4 \left[(5*x-x^2)+x\right]\,dx$$ which sums the functions instead of finding their difference.

Answer

Calculating $$\int_0^4 \left[x-(5*x-x^2)\right]\,dx$$ which would yield a negative area if not corrected.

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