Find the integral 2*piint(xx^2)dx&0&5

 Exercise

$2\pi\int_0^5\left(x\cdot x^2\right)dx$

 

When multiplying exponents with same base you can add the exponents: $x\cdot x^2$

$2\pi \int_{0}^{5} x^{3}dx$

 

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $3$

$\left[2\pi \left(\frac{x^{4}}{4}\right)\right]_{0}^{5}$

 

Simplify the expression

$\left[\frac{\pi }{2}x^{4}\right]_{0}^{5}$

 

Evaluate the definite integral

$\frac{\pi }{2}\cdot 5^{4}- \left(\frac{\pi }{2}\right)\cdot 0^{4}$

 

Simplify the expression

$\frac{625\pi }{2}$

$\frac{625\pi }{2}$

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