Evaluate the Integral

Problem

(∫_0^4)(x3*d(x))

Solution

1. Identify the integrand and the limits of integration. The function to integrate is ƒ(x)=x3 and the interval is [0,4]

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

3. Find the antiderivative of x3 by increasing the exponent by 1 and dividing by the new exponent.

(∫_^)(x3*d(x))=(x4)/4

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

[(x4)/4]40=4/4−0/4

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

256/4−0=64

Final Answer

(∫_0^4)(x3*d(x))=64

Want more problems? Check here!