Evaluate the Integral

Problem

(∫_0^2)(5*x^2*d(x))

Solution

1. Identify the constant and the power of x in the integrand.

2. Apply the power rule for integration, which states that (∫_^)(x^n*d(x))=(x^(n+1))/(n+1)

3. Factor out the constant 5 and integrate x^2 to get (5*x^3)/3

4. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit 2 and the lower limit 0

5. Substitute the limits into the expression: (5*(2)^3)/3−(5*(0)^3)/3

6. Simplify the numerical expression to find the final value.

Final Answer

(∫_0^2)(5*x^2*d(x))=40/3

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