Evaluate the Integral

Problem

(∫_0^b)(9*x8*d(x))

Solution

1. Identify the integrand and the limits of integration. The function to integrate is 9*x8 and the limits are from 0 to b

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

(∫_^)(9*x8*d(x))=9⋅(x9)/9

3. Simplify the expression by canceling the constant factor 9

9⋅(x9)/9=x9

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

[x9]b0=b9−0

5. Simplify the final numerical result.

b9−0=b9

Final Answer

(∫_0^b)(9*x8*d(x))=b9

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