Evaluate the Integral

Problem

(∫_0^10)(4*x2+7*d(x))

Solution

1. Identify the integral as a definite integral of a polynomial function.

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

3. Find the antiderivative of the expression 4*x2+7

(∫_^)(4*x2+7*d(x))=(4*x3)/3+7*x

4. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit of 10 and the lower limit of 0

[(4*x3)/3+7*x]100

5. Substitute the upper limit into the expression.

(4*(10)3)/3+7*(10)=4000/3+70

6. Substitute the lower limit into the expression.

(4*(0)3)/3+7*(0)=0

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

4000/3+210/3=4210/3

Final Answer

(∫_0^10)(4*x2+7*d(x))=4210/3

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