Solve pi ∫ (from 0 to 4) of y^2 wrt y+piint_4^6(3)^2dy-piint_0^6y^2/4dy

$$\pi \int _ { 0 } ^ { 4 } y ^ { 2 } d y + \pi \int _ { 4 } ^ { 6 } ( 3 ) ^ { 2 } d y - \pi \int _ { 0 } ^ { 6 } \frac { y ^ { 2 } } { 4 } d y$$

Factor

$$\frac{64 \pi}{3} = 67.02064327658225$$

Solution Steps

Factor out \pi .

$$\pi \left(\int _{0}^{4}y^{2}\mathrm{d}y+\int _{4}^{6}9\mathrm{d}y-\int _{0}^{6}\frac{y^{2}}{4}\mathrm{d}y\right)$$

Evaluate

$$\frac{64\pi }{3}\approx 67.020643277$$