Provide an appropriate response.
-Given use properties of definite integrals to evaluate
A) 18
B) 24
C) 13
D) 54

Question

Provide an appropriate response.
-Given  use properties of definite integrals to evaluate 
A) 18 
B) 24 
C) 13 
D) 54

Quizplus · Accepted Answer

Since the definite integral of the given function is being asked, we can use the properties of integrals to solve it. Firstly, we can simplify the integral by factoring out the constant 4 from the integrand, giving us:

4∫(x^2 + 2x + 3) dx

Using the power rule of integration, we can find the antiderivative of each term inside the integrand:

4[(x^3/3) + (x^2) + (3x)] evaluated from x = -1 to x = 2

Plugging in the upper and lower limits of integration, we get:

4[((2)^3/3) + (2^2) + (3)(2)] - 4[((-1)^3/3) + (-1^2) + (3)(-1)]

This simplifies to:

4[(8/3) + 4 + 6] - 4[(-1/3) - 1 - 3]

Which further simplifies to:

(32/3) + 16 + 24 + (4/3) + 4 + 12

Adding all these terms together, we get:

18

Therefore, the answer is A) 18.

Provide an Appropriate Response