Question

Find the area of the region bounded by y=5-x², x=2, x=3 and X-axis.

Answer 1

5-4=1
5-9=-4
May be it is helpful to uh

Answer 2

see the rough daigram as shown in figure.
we can say that area enclosed by curves = $|\int\limits^2_{\sqrt{5}}{5-x^2}\,dx|+|\int\limits^3_{\sqrt{5}}{5-x^2}\,dx|$

= $|\left[\begin{array}{c}5x-\frac{x^3}{3}\end{array}\right]^2_{\sqrt{5}}|+|\left[\begin{array}{c}5x-\frac{x^3}{3}\end{array}\right]^3_{\sqrt{5}}|$

=$|5(2-\sqrt{5})-\frac{2^3}{3}+\frac{\sqrt{5}^3}{3}|+|5(3-\sqrt{5})-\frac{3^3}{3}+\frac{\sqrt{5}^3}{3}|$

=$|10-5\sqrt{5}-\frac{8}{3}+\frac{5\sqrt{5}}{3}| + |15-5\sqrt{5}-9+\frac{5\sqrt{5}}{3}|$

=$|\frac{22}{3}-\frac{10\sqrt{5}}{3}|+|6-\frac{10\sqrt{5}}{3}|$

=$\frac{20\sqrt{5}}{3}-\frac{40}{3}$