Evaluate the Integral

Problem

(∫_−1^2)(x3*d(x))

Solution

1. Identify the integrand and the limits of integration. The function is ƒ(x)=x3 and the interval is [−1,2]

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

(∫_^)(x3*d(x))=(x4)/4

3. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit 2 and subtracting the evaluation at the lower limit −1

[(x4)/4]2(−1)=((2)4)/4−((−1)4)/4

4. Simplify the numerical expression.

16/4−1/4

5. Calculate the final difference.

15/4

Final Answer

(∫_−1^2)(x3*d(x))=15/4

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