Question

Use geometry to find the area A under the graph of the function f(x)=x+6 from 1 to 5 . (Give an exact answer using fractions if needed.)

Answer 1

36 unit^2.

Explanation:

f(x) = x + 6

When x = 1 f(x) = 7

when x = 5, f(x) = 11.

The area under the Graph is a trapezium with part of the x axis as the perpendicular distance between the 2 parallel lines.

The length of the parallel sides are 7 and 11 units and the distance between them is 5-1 = 4 units long .

So the required area

A = 1/2 * 4(7+11)

= 1/2 * 72

= 36 unit^2.