Determine the area bounded by the curve y = 3x^2 + 6x + 7 and the X-axis between the ordinates x = 5 and x = 10 .

Step-by-step solution

The required area is given by the definite integral of the curve y = 3x^2 + 6x + 7 from x = 5 to x = 10 . A = ₅¹⁰ (3x^2 + 6x + 7) dx Integrating the function with respect to x : A = [ x^3 + 3x^2 + 7x ]₅¹⁰ Substituting the upper and lower limits: A = (10^3 + 3(10)^2 + 7(10)) - (5^3 + 3(5)^2 + 7(5)) A = (1000 + 300 + 70) - (125 + 75 + 35) A = 1370 - 235 A = 1135