The function f (x) is defined as f (x) = {(-1, x ≤ 0),( (x + 2) ^ 2, 0 < x ≤ 3),(x, x > 3):}. The area under the f (x) curve between x = (-2) and x = 5 is? Options: a) 27 b) 205/3 c) 155/3 d) 80

Is it to be solved using application of integral? Please help.

1 Answer
Mar 29, 2018

The answer is none of the above.

Explanation:

This function should be relatively easy to graph, so I would give that a try.

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So pretty much, we have a rectangle with height -1 and width 2, the area under the parabola (x +2)^2 on [0, 3] and a trapeze with b_1 = 5, b_2 = 3, h = 2.

So our expression for area will be

A = (2)(-1) + int_0^3 x^2 +4x + 4dx + ((5 + 3)(2))/2

A = 6 + int_0^3 x^2 + 4x + 4 dx

A = 6 + [1/3x^3 + 2x^2 + 4x]_0^3

A = 6 + 1/3(3)^3 + 2(3)^2 + 4(3)

A = 6 + 9 + 18 + 12

A = 45

Hopefully this helps!