Find the area under the curve given by f(x) = 3x2+ 5x

Question

Find the area under the curve given by f(x) = 3x²+ 5x                                               8marks

Answer 1

To find the area under a curve you need to integrate the function defining the curve.

Assuming that, by 3x2 you really mean 3x²

   and not  3x2 which could be = 6x or =6 depending on if the x is a variable or the times sign.

 

integral f(x) dx = int(3x² + 5x)dx

 

= 3 int(x²)dx + 5 int(x)dx

 

= 3  1/3(x³⁾  +  5  1/2(x²)

 

= x³ + (5x²)/2 + Constant

 

We probable should really do a definite integral and remove the constant,

is there a domain defined for the function so we would kow what points to integrated between?

Answer 2

f(x) = (3x + 5) x, they might want the area bounded above the curve and below the x-axis...? (Just a guess.) In that case, you could integrate between x = -5/3 and 0.

 

In general, you need a bounded region to find an area. (There are exceptions to this: see convergent indefinite integrals.)