Question

Asked Apr 15, 2019

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For the function f whose graph given below, compute f (x) dx on the interval (-1,4)

Step 1

Since we have to find the integral of f(x).dx over x = -1 to x = 4, we have to necessarily find the total area under f(x) and x - axis over the range x =-1 to x = 4.

Since, f(x) has multiple points of inflexion, let's break the entire area at every integral point of x axis. Hence, the overall area has been broken into five areas A1 to A5 and the break lines had been shown in red line in the diagram above.

Step 2

Hence, integral of f(x).dx (over x = -1 to x = 4) =A1 + A2 + A3 + A4 + A5

A1 = area of a triangle of base 1 unit and height 1 unit = 1/2 x 1 x 1 = 0.5

Si...

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