Find area bounded by f(x) = 20 + x - x^2 and g(x) = x^2 - 5x over [1,3]
Since I will have to account for the negative area defined by g(x) = x^2 - 5x and y = 0, I will denote the area bounded by f(x) over [1,3] as A1 and g(x) over [1,3] as A2
A1 = \(\displaystyle \int_1^{3} 20 + x - x^2\,dx = \frac{106}{3}\)
A2 = \(\displaystyle \int_1^{3} x^2 - 5x = \frac{-34}{3}\)
But when I add these two areas together, I don't get the same answer as my book. My book says the answer to this problem is \(\displaystyle \frac{343}{3}\)
Any help would be appreciated. What am I doing wrong?
Since I will have to account for the negative area defined by g(x) = x^2 - 5x and y = 0, I will denote the area bounded by f(x) over [1,3] as A1 and g(x) over [1,3] as A2
A1 = \(\displaystyle \int_1^{3} 20 + x - x^2\,dx = \frac{106}{3}\)
A2 = \(\displaystyle \int_1^{3} x^2 - 5x = \frac{-34}{3}\)
But when I add these two areas together, I don't get the same answer as my book. My book says the answer to this problem is \(\displaystyle \frac{343}{3}\)
Any help would be appreciated. What am I doing wrong?
