Solve 2 pi ∫ (from 0 to 3) of (x^2+3)x wrt x+2piint_0^3(x^2-x^2+2x+7)dx

$$2 \pi \int _ { 0 } ^ { 3 } ( x ^ { 2 } + 3 ) x d x + 2 \pi \int _ { 0 } ^ { 3 } ( x ^ { 2 } - x ^ { 2 } + 2 x + 7 ) d x$$

Factor

$$\frac{255 \pi}{2} = 400.5530633326986$$

Solution Steps

Factor out 2.

$$2\left(\pi \int _{0}^{3}\left(x^{2}+3\right)x\mathrm{d}x+\pi \int _{0}^{3}x^{2}-x^{2}+2x+7\mathrm{d}x\right)$$

Consider \pi \int _{0}^{3}\left(x^{2}+3\right)x\mathrm{d}x+\pi \int _{0}^{3}x^{2}-x^{2}+2x+7\mathrm{d}x. Factor out \pi .

$$\pi \left(\int _{0}^{3}\left(x^{2}+3\right)x\mathrm{d}x+\int _{0}^{3}x^{2}-x^{2}+2x+7\mathrm{d}x\right)$$

Rewrite the complete factored expression.

$$2\pi \left(\int _{0}^{3}\left(x^{2}+3\right)x\mathrm{d}x+\int _{0}^{3}x^{2}-x^{2}+2x+7\mathrm{d}x\right)$$

Evaluate

$$\frac{255\pi }{2}\approx 400.553063333$$