Question:

Compute the definite integral: ∫_1^3 (4x^2 - 2x + 5) dx

Answer: To find the definite integral of the given function, we need to first find the antiderivative of each term and then apply the fundamental theorem of calculus to evaluate the integral.

Step 1: Find the antiderivative of each term: Using the power rule, the antiderivative of 4x^2 is (4/3)x^3, the antiderivative of -2x is -x^2, and the antiderivative of 5 is 5x.

Step 2: Apply the fundamental theorem of calculus: Now, we can evaluate the definite integral: ∫_1^3 (4x^2 - 2x + 5) dx = [(4/3)x^3 - x^2 + 5x]_1^3 = [(4/3)(3)^3 - (3)^2 + 5(3)] - [(4/3)(1)^3 - (1)^2 + 5(1)] = [36 - 9 + 15] - [4/3 - 1 + 5] = 42 - 4/3 + 11 = 46 - 4/3

Therefore, the value of the definite integral is 46 - 4/3.