Final Answer
$\frac{5y^{3}}{5832}$
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Step-by-step Solution
Problem to solve:
$\int_{0}^{\frac{y}{6}}\frac{5}{6}\cdot x\cdot\frac{2}{3}\cdot xdx$
Specify the solving method
1
Simplifying
$\int_{0}^{\frac{y}{6}}\frac{5}{9}x\cdot xdx$
Learn how to solve definite integrals problems step by step online.
$\int_{0}^{\frac{y}{6}}\frac{5}{9}x\cdot xdx$
Learn how to solve definite integrals problems step by step online. Integrate the function 5/6x*2/3x from 0 to y/6. Simplifying. When multiplying two powers that have the same base (x), you can add the exponents. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. 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 2.
Final Answer
$\frac{5y^{3}}{5832}$