GATE 2026 IN – Question 57

Signals and Systems · Signals and linear time-invariant systems · 2 marks · Numerical answer

Let $$f(t)=\begin{cases}1,&t\in[0,2],\\-t+3,&t\in[2,3],\\0,&\text{otherwise}.\end{cases}$$

Then $\displaystyle\int_{-\infty}^{\infty}f(\tau)\,d\tau=$ ________. (Rounded off to one decimal place.)

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Correct answer: 2.4 to 2.6

Explanation

The contribution from 0 to 2 is a rectangle with area $2\times1=2$. From 2 to 3, the signal falls linearly from 1 to 0, forming a triangle with area $\tfrac12\times1\times1=0.5$.

There is no contribution outside these intervals. The integral is **2.5**.