Evaluate the Integral

Problem

(∫_0^2)(5*x2*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 (∫_^)(xn*d(x))=(x(n+1))/(n+1)

3. Factor out the constant 5 and integrate x2 to get (5*x3)/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*x2*d(x))=40/3

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