Discussion Forum

The area bounded by f(x) = x² , 0≤x≤1, g(x) = -x+2, 1≤x≤2 and x- axis is 

Answer:

Explanation:

Required area = Area of OAB + Area of ABC

Now, Area of OAB = $\int_{0}^{1}f(x)dx+\int_{1}^{2}g(x)dx$

= $\int_{0}^{1}x^{2}dx+\int_{1}^{2}(-x+2)dx$

= $\frac{x^{3}}{3}\mid_0^1$ + $\left[\frac{-x^{2}}{2}+2x\right]_1^2$

= $\frac{1}{3}+\left[\left(\frac{-4}{2}+4\right) - \left(\frac{-1}{2}+2\right)\right]$

= $\frac{1}{3}+\left[\left(-2+4\right) - \left(\frac{3}{2}\right)\right]$

= $\frac{1}{3}+\frac{1}{2}$ = $\frac{5}{6}$ Sq.Unit