Solve 2pi[2x^3/3+9x^2/2+9]_1^3dx

$$2 \pi [ \frac { 2 x ^ { 3 } } { 3 } + \frac { 9 x ^ { 2 } } { 2 } + 9 ] _ { 1 } ^ { 3 } d x$$

Evaluate

$$\frac{\pi \left(4x^{3}+27x^{2}+54\right)}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2x^{3}}{3} times \frac{2}{2}. Multiply \frac{9x^{2}}{2} times \frac{3}{3}.

$$2\pi \left(\frac{2\times 2x^{3}}{6}+\frac{3\times 9x^{2}}{6}+9\right)$$

Since \frac{2\times 2x^{3}}{6} and \frac{3\times 9x^{2}}{6} have the same denominator, add them by adding their numerators.

$$2\pi \left(\frac{2\times 2x^{3}+3\times 9x^{2}}{6}+9\right)$$

Do the multiplications in 2\times 2x^{3}+3\times 9x^{2}.

$$2\pi \left(\frac{4x^{3}+27x^{2}}{6}+9\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{6}{6}.

$$2\pi \left(\frac{4x^{3}+27x^{2}}{6}+\frac{9\times 6}{6}\right)$$

Since \frac{4x^{3}+27x^{2}}{6} and \frac{9\times 6}{6} have the same denominator, add them by adding their numerators.

$$2\pi \times \frac{4x^{3}+27x^{2}+9\times 6}{6}$$

Do the multiplications in 4x^{3}+27x^{2}+9\times 6.

$$2\pi \times \frac{4x^{3}+27x^{2}+54}{6}$$

Cancel out 6, the greatest common factor in 2 and 6.

$$\frac{4x^{3}+27x^{2}+54}{3}\pi$$

Express \frac{4x^{3}+27x^{2}+54}{3}\pi as a single fraction.

$$\frac{\left(4x^{3}+27x^{2}+54\right)\pi }{3}$$

Use the distributive property to multiply 4x^{3}+27x^{2}+54 by \pi .

$$\frac{4x^{3}\pi +27x^{2}\pi +54\pi }{3}$$

Expand

$$\frac{4\pi x^{3}}{3}+9\pi x^{2}+18\pi$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2x^{3}}{3} times \frac{2}{2}. Multiply \frac{9x^{2}}{2} times \frac{3}{3}.

$$2\pi \left(\frac{2\times 2x^{3}}{6}+\frac{3\times 9x^{2}}{6}+9\right)$$

Since \frac{2\times 2x^{3}}{6} and \frac{3\times 9x^{2}}{6} have the same denominator, add them by adding their numerators.

$$2\pi \left(\frac{2\times 2x^{3}+3\times 9x^{2}}{6}+9\right)$$

Do the multiplications in 2\times 2x^{3}+3\times 9x^{2}.

$$2\pi \left(\frac{4x^{3}+27x^{2}}{6}+9\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{6}{6}.

$$2\pi \left(\frac{4x^{3}+27x^{2}}{6}+\frac{9\times 6}{6}\right)$$

Since \frac{4x^{3}+27x^{2}}{6} and \frac{9\times 6}{6} have the same denominator, add them by adding their numerators.

$$2\pi \times \frac{4x^{3}+27x^{2}+9\times 6}{6}$$

Do the multiplications in 4x^{3}+27x^{2}+9\times 6.

$$2\pi \times \frac{4x^{3}+27x^{2}+54}{6}$$

Cancel out 6, the greatest common factor in 2 and 6.

$$\frac{4x^{3}+27x^{2}+54}{3}\pi$$

Express \frac{4x^{3}+27x^{2}+54}{3}\pi as a single fraction.

$$\frac{\left(4x^{3}+27x^{2}+54\right)\pi }{3}$$

Use the distributive property to multiply 4x^{3}+27x^{2}+54 by \pi .

$$\frac{4x^{3}\pi +27x^{2}\pi +54\pi }{3}$$