Multiple choice

The following plot shows a function y which varies linearly with x. The value of the integral I = $\int\limits_1^2 y \hspace{0.2cm}dx$is

  1. 1.0

  2. 2.5

  3. 4.0

  4. 5.0

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\text{The given plot is straight line with equation is} \\ \frac{x}{-1}+ \frac{y}{1} = 1 \\ or \hspace{1cm} y = x + 1 \\ Now \hspace{1cm} I = \int\limits_1^2 ydx = \int\limits_1^2 (x + 1) dx \\ = \bigg[\frac{(x+1^2)}{2}\bigg]^2 = \frac{9}{2} - \frac{4}{2} = 2.5$