Evaluate the Integral

Problem

(∫_0^2)(2*x2*d(x))

Solution

1. Identify the constant and the power of x in the integrand 2*x2

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

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

(∫_^)(2*x2*d(x))=(2*x3)/3

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

[(2*x3)/3]20

5. Substitute the upper limit into the expression.

(2*(2)3)/3=(2*(8))/3=16/3

6. Substitute the lower limit into the expression.

(2*(0)3)/3=0

7. Subtract the lower limit value from the upper limit value.

16/3−0=16/3

Final Answer

(∫_0^2)(2*x2*d(x))=16/3

Want more problems? Check here!